Some un-official software allows you to run plugins natively in the game. These plugins and the software used to run them are not run or maintained by Mojang Studios.
Some un-official software allows you to run modded versions of the game. These mods and the software used to run them are not run or maintained by Mojang Studios.
Fabric, unlike Forge, is not based on the MCP. This allows it to be updated for snapshots easier. It is incompatible with Forge.
Plugins + Mods
Some un-official software allows you to run modded versions of the game as well as plugins. These mods, plugins and the software used to run them are not run or maintained by Mojang Studios.