Dimensional Differences (UcAM)
The Empty (see also: the void, nothing)
Before there was the universe, or God and Amara, or matter, or time, there was nothing. There was The Empty. Because there is nothing there, that means that it could be anything (and we know that at some point it does form everything by way of god and Amara). It's endless possibility and potential. In this way, it can be thought of as zero dimensional (0D) or infinitely dimensional (∞D). (technically this would be "located" outside of the known universe(s), if you can define a lack-thereof as being located somewhere. It's all that is not.) The Shadow is, and is a creature of, the Empty. It acts as a ruler and warden. It is my belief that the Shadow did not actually exist until Jack woke Castiel up. Definition kills infinity and murders potential, which is why the Empty becomes a place and develops a personhood, as well as losing some of, what should be, its untouchable status. (Cas does get killed and brought back multiple times before this, but all prior deaths had vessel shenanigans going on, and didn't necessarily give him true death)
The Empty is the all consuming nothing that the concept of creation itself is fighting against. All creations are an intrusion. Going to the Empty is returning to a 'place' before creation, and thus should be considered a true death.
Heaven (see also: ethereal plane)
Heaven was the first place that was created. It was made for —or formed around— the archangels and god. As it was made for primordials, it's not suited for lesser beings; they weren't even in consideration at that point. Being the first of its nature and coming out of the potential of anything, heaven is also full of possibility and lacking in proper definition, at least by the standards of 3D creatures. The rules of 3D reality and physics need not apply. Can be seen as four (or more!) dimensional (4D).
There are several locations within heaven, but they are for the most part separated into 'for angels' and 'for humans'. Heaven is said to be powered by the grace of angels, using them as 'batteries' in order to 'keep the lights on.' (This is capable of burning through all the grace that an angel has, eventually, which may be part of the reason the lesser angels were created.) In the parts that are 'for angels' (like the throne room, the hallways, the offices, the prison, etc.), grace is the primary building block. The parts that are 'for humans' are made of human souls, being that each individual 'paradise' is a person's memories. Though souls aren't being used as a power source for heaven*, they have a stabilizing effect, which helps prevent the dimension from collapsing into the void. (*human souls don't power heaven, as in keep it from falling apart, but they may be part of what powers angels, or at least rejuvenates them. We know that angels can and will choose to spend time in personal heavens, like with Castiel and Raphael)
There's also the Garden. Ash calls it the 'core' of heaven. This is possibly where everything started, and was first 'grown' (similar to the garden of Eden being the start of humanity. Note that the Garden and Eden are not the same place, though some souls interpret the Garden as Eden). Another point to it being the oldest part (and therefore the closest to god) is the fact that the primary resident, Joshua, is able to hear god directly, which is otherwise something only archangels really do.
Earth (see also: the material plane, the known universe)
Earth, being the most central to the story, is the primary focus, however this also applies to the entirety of the universe that earth is found in. After Amara was sealed away and archangels were created to do so, god began experimenting with creations. He started creating things he never had before. Death even makes reference to this being a 'petri dish'.
This is by far the most stable and concrete realm in existence, and may be the primary tool in the fight against the void. Unlike all the other planes, this one's got self perpetuation. It feeds into heaven, hell and purgatory, bolstering each of those planes and pushing itself farther/further from the Empty. Lots of layers to get through.
As we all know, earth is three dimensional (3D) and the reason that 3D is more stable than 4D or 2D is probably the same reason that a three legged stool (and pretty much only a three legged stool) can be stable no matter how uneven the ground is.
Purgatory (see also: monster jail)
Purgatory is the next place created, as it was made to contain the Leviathan, the first beasts. Death says the god put them away because he was afraid that they would consume and destroy all of his subsequent creations. Because the Leviathans were first creatures of earth, they too would be 3D (approximately. They're pretty unstable and don't themselves seem to self perpetuate, but they're also very much a first draft). Therefore, purgatory is also approximately 3D. Which is why creatures such as humans can run around and interact with it, despite it being older than angels.
Similar to the Shadow, Eve is of purgatory and acts as some type of power of authority over the realm and its souls*. Purgatory was originally created as a monster jail, and it is this connection to that that makes monsters —children of Eve— go to purgatory when they die, as opposed to heaven, hell, or the Empty. (*While Eve has an unknown connection to the Leviathan, she does not have control or power over them. As Death said, the Leviathan are "older than souls".)
Hell comes around after all the rest, and is created as a result of Lucifer damning human souls. He is then cast into the Cage, and similar to the Garden, hell subsequently sprung from there. Due to it being made for Lucifer (aka an archangel) the Cage would be at least partially 4D (making it both difficult to find and why all inhabitants of the don't necessarily show up to lesser beings that approach it).
Hell is strange and appears to have sections that are 3D, as well as places that are more abstract and possibly two dimensional (2D), such as where Dean was tortured. Possibly 2D, because hell is not only formed of malicious and ill intents, but the malicious and ill intents of demons, which are cooked down and simplified creatures. Hell may also reflect heaven in the way that it is partially made up of human souls, only reliving a version of their worst memories instead of their best ones.
Similar to purgatory, it acts as a prison not only for Lucifer, but for damned souls/demons. (Similar to Eve, the connection to the 'parent' is what draws them towards the specific realm)
The Axis Mundi (see also: the path, the road, the river)
The Axis Mundi is what connects the realms together. It appears differently to the souls in heaven, seeing it as different pathways. This is what allows souls to travel between realms, and isn't generally for use of angels.
One of the special properties of reapers, however, is access to and ability to traverse this pathway. They need to, as they have to guide souls to their destinations, but it also allows them to easily hop between realms, and even bring living people.
Along with linking heaven, earth, hell, and purgatory, it also has some sort of back door into the Empty, as Billie(before she becomes Death) tells Dean that the next time he or Sam die, whatever reaper collects collects them will be sending them to the Empty)
