Some Hockey 101 for those who like to write accurate smut
I mentioned to some friends a couple of hockey things I noticed a lot of fics getting wrong, and got encouraged to write this post. I want to be clear that this is not a shaming post or a callout! You don't need to know hockey to write hockey smut! There's plenty of stuff that the book and even the show—(which really had no excuse, there's no way they didn't have a hockey consultant)—gets wrong.
But if you WANT to get stuff right, here goes.
Games are 60 minutes, divided into three 20-minute periods. So players will talk about "thirds" of the game and "periods" not halfs or quarters, etc.
(Yes, this is directed toward the one person I saw with a fic where something happened in "the third quarter" of the game. I love you, your fic was great).
In the NHL, teams suit 20 players for a team—usually 12 forwards (four lines of three men each), 6 defensemen (who play in pairs) and 2 goalies. Some teams will play with three forward lines, seven defensemen, and a couple of alternate forwards who shift in and out of the three forward lines. All the players except the goalie will play in shifts that are usually like a minute or three long. This means that players OTHER than the goaltender will get between 10-25 minutes of “ice time” a game. Defensemen usually get more ice time. How much ice time each player gets is a matter of much discussion and analysis—the more you get, the more your team values you, but really high ice time can also mean that a team doesn’t have enough depth on the bench and is risking burning out their star players. 
Since the goaltender is out there the whole night, they suit a backup in case he's injured or just has a bad night. There can be a lot of drama over pulling a goaltender—every goalie has the occasional bad night, but if he gets pulled for giving up a goal that he doesn't think was his fault he may get mad, or conversely, if he doesn't get pulled when he's clearly off his game, he may also get mad. See Patrick Roy.
Positions
There are six player positions, and six players usually on the ice:
Goaltender
Left wing (forward)
Right wing (forward)
Center (forward)
Right defenseman (blueliner)
Left defensemen (blueliner)
However, the goalie isn't usually counted when teams talk about players on the ice, so when we talk about "five players" that's the five numbered positions above.
Forwards and defensemen can generally swap around for other forward or defense positions (e.g., a left wing can play right wing, a right defenseman can play on the left), although there are players (like Shane) who have always played center or one side or another and would find it difficult to adjust to a move.
Those are the only six positions. Any other role that someone mentions is a more specific type of the five above. So, for example, there are "offensive defensemen" who take a regular defense position but really like to jump up into the play and score goals and assists. "Star" or "power" forwards are just a specific type of forward, not an actual position on the ice. When people talk about enforcers, that's a description of the function they play on the team (e.g., a player who is good at delivering massive hits and getting into fights and will do that specifically against opposing players if they cross the unwritten rules of the game). An enforcer is usually a wing on the third or fourth line. It's not an actual position on the ice.
(Yes, this directed to the person who had Ilya lecture JJ that he should be an enforcer instead of a left wing. Those aren't mutually exclusive—far from it, in fact. I love you, your fic was amazing.)
Ilya is not an enforcer, and would almost certainly not be getting into a ton of fights. Like, two or three a season, sure—he's the captain and he's an asshole, so it'd happen occasionally—but not every game. It might happen because he taunts a player until they attack him—that's part of the game, he draws a two-minute minor penalty for fighting, but the other player draws a two-minute minor for instigating, a five-minute major for fighting, and potentially a ten-minute game misconduct—or because he's fighting the captain of the other team or a defenseman who was deliberately targeting him.
A "Gordie Howe hat trick" is when a player scores a goal, an assist, and a fight in the same game :D Ilya would love those so much.
There's a final descriptor for a player that I've rarely seen used in fics, which is a "pest" (which Ilya actually fits in much better than as an enforcer, although again, he's too talented to be primarily described this way). Pests are players who try to deliberately taunt and insult opposing players (with "chirps" i.e., on-ice insults, or just annoying play that doesn't quite cross the line into being a penalty) in order to get the opposing players to retaliate in some way that draws a penalty. Again, they're usually wings on the third or fourth line. Those lines are often made up of just enforcers + pests, whose job is to go out and make it hard to score for the opposing team's top lines.
Penalties and special teams
Normal hockey is played 5-on-5 (again, not counting goalies). When there's a penalty, a player will be put in the penalty box for 2, 4, or 5 minutes (minor, double-minor, major), and the team has to play without that player (5-on-4 hockey, e.g., only four players + goaltender on the ice for one team, while the other team. has five + the goalie) until the penalty is up. You can have multiple penalties, so 5-on-3, 4-on-4, 4-on-3, etc., are all situations that can happen and that teams will train for. When playing 5-on-4, a team will usually put out four forwards and one blueliner, so this is a scenario when you'd often get two centers out at the same time.
Additionally, a team can, at any point, pull their goaltender and put six regular players on the ice (normally four forwards + two defensemen) to try and catch up when they're behind (6-on-4 or "empty net" play). This is NORMALLY only done in the last few minutes of a game, and NORMALLY when a team is only one goal behind. It's unusual to see an empty situation any other time or when a team is 2 or more goals behind, although it'll happen (and some rare teams have specifically trained for it and are known for pulling their goaltender with like, ten minutes of play remaining. But again. rare). The game doesn't stop in order for this to happen—the goaltender will just get waved off and as soon as his feet leave the ice, another forward will jump on to replace him.
Playing with a player advantage is called being on the power play, or just a power play (e.g., "Boston's on the power play" or "Boston is going to get a power play"). Playing with a disadvantage is called being shorthanded.
Players who normally go out during the power play or when shorthanded ("penalty killers") are called "special teams." So you'll frequently hear players saying that the "special teams really showed up today" or "we need to work on our special teams." Normal lines get disrupted for special teams, so if Ilya and Shane are on the same team, you might see them center the first and second lines during normal play but then partner up for the power play. The players who are out during a power play are not necessarily the same ones who will be out during a penalty kill—e.g., there isn't a specific "special team" within a team that does it all, which is why it's usually pluralized.
Playoffs
Okay, this is one of the more egregious places I see people getting things wrong, so suit up. :D
First, the playoffs are four rounds. Each round is a best of seven series, so a team needs FOUR wins to advance to the next round—not three. There is no way to win the series before Game 4. It's most common for the series to end in Game 5 or Game 7, but Games 4 and 6 happen to. If it ends in Game 4 (meaning one team won four games in a row and the other team won none), it's called a sweep. This means a team needs 16 wins to get the Stanley Cup, and might need to play as much as 28 games to do it.
Second, the NHL (and yes, also the MLH, this is specifically called out in Svetlana's analysis in episode 2) is split into two conferences—East and West. Each conference is split into two divisions. Eight teams make the playoffs for each conference—the top three teams in each division and two "wild cards." So, sixteen teams total. The first two rounds are within divisions (except for potentially one wild card who would get bracketed with the other division). In the third round the champion of each division plays the champion of the other division within their conference, and in the fourth round (the Stanley Cup finals, or in the show, the "MLH Cup finals"), the champion of each conference plays the champion of the other conference.
E.g, the bracket looks like this:
Boston and Montreal are divisional rivals, both within the Atlantic division, which means they are almost always going to meet in the first or second round. The only way they meet in even the third round is if one of them wins the Atlantic division and the other is a wild card, and they will never play each other in the Stanley Cup Finals.
Montreal and Boston CAN NEVER PLAY EACH OTHER FOR THE MLH CUP. Period. No. It cannot happen. They will ALWAYS meet each other earlier than that. I am so sorry to all the people who want to see Ilya or Shane on the ice when the other wins the Stanley Cup, but it cannot happen unless one of them moves to the Western Conference (or they're playing on the same team, of course!).
New York is also in the Eastern Conference. Ottawa is also in the Eastern Conference. None of these teams will ever play each other in the Stanley Cup Finals.
If you want to see that happen, I highly encourage moving Shane to Vancouver (given that his mom is of Japanese ancestry, highly likely he has family/ancestral ties there) or Los Angeles (for Rose?). Or have Ilya go off to a Western team in a snit! Or trade one of them (unlikely though that would be, teams don't usually trade their captains unless something's pretty messed up... Like one of them coming out as gay, of course). And speaking of which...
Trades
Teams can and do trade players, but it rarely happens within divisions. Teams usually trade to other divisions or other conferences so there's less chance of players frequently playing their old teams. Star players usually have clauses in their contracts that give them partial or full veto over whether and where they can be traded ("no trade" clauses).
Draft picks can also be traded—teams receive draft picks based on how well they're doing (e.g., the teams that do the worst receive the most and earliest draft picks, so they can build up better teams).
So, yes, theoretically, you can have Shane or Ilya get traded to the other team, but it would be very unusual and need to have a lot of justification for why the team is doing it and (if it's later in their careers when their rookie contracts would have run out), why the player is waiving their no-trade clauses.
Players can also ask their team to trade them, and that team usually will. See, for example, Patrick Roy or Ray Bourque.
