Alright so.
Weapon X/Weapon 10 - the series of experiments where they put metal on Logan's bones and tortured him and put a bunch of machinery on him as portrayed in the Marvel Comics Presents arc "Weapon X" (also simply known as Experiment X). Also the name Weapon Plus operated under for years/the continuation of the original Weapon Plus program. This program included experiments on Mutants and humans alike to try and create more supersoldiers, study Mutants and superpowers in general. Team X was a part of this section of the Weapon Plus program. Their facility was located in Canada.
Weapon Plus - the actual name of the program the Weapon X experiments were a part of. Was revealed to have been involved in the creation of Captain America (Weapon 1/I). Characters experimented on/created in Weapon Plus include Fantomex, the Stepford Cuckoos, and Typhoid Mary. Romulus and John Sublime were behind many of the program's experiments and Weapons. Involved with at least a few governments.
The Facility - Not a direct offshoot of the Weapon X program, but rather pieces and bits of things that were apart of the program. Less militarized than its predecessors, more of a personal business-based organization. Main goal is creation of assassins and killing machines. The Facility created Kimura, Laura Kinney and the Predators X.
Random Alchemax scientists - Created mostly unsuccessful clones of Laura Kinney (Gabby, Bellona, Zelda, etc).
Team X - The execution of the Weapon X experiments' goals. A team of operatives carrying out missions in secret for the C.I.A. The operatives (including Wolverine, Sabretooth, Maverick, John Wraith and Silver Fox, among others) were manipulated and had fake memories implanted in their minds. This team notably fought Omega Red.
Department K - An offshoot of the Weapon X experiments run by the Canadian Government. Responsible for the creation of Deadpool.
Weapon X (Age of Apocalypse) - Logan's codename in the Age of Apocalypse.
Weapon X Team - A project ran by Malcolm Colcord with similar goals to the original Weapon X program. This new program established a Mutant concentration camp in Canada where Mutants were experimented on, studied, and executed. The Project also included a team of Mutant operatives, some recruited willingly, other forced in, who were meant to tie up loose ends of the former programs and hunt "failed experiments". Members of this team included Marrow, Aurora (forced into the ordeal), Chamber (a spy for the X-Men), Sabretooth, Maverick, and Sauron. They fought Cable's Underground (who some members of the program were working with). The program was torn apart from the inside and abandoned.
Weapon X (Kane) - Garrison Kane, a assassin experimented on by Department K. Went by the name Weapon X.
Weapon X-Men - A team consisting of Chamber, Thunderbird, Cable and Wolverine that didn't do much.
