The basics :
NG = New Game (doing a run with a fresh, new file) NG+ = New Game+ (doing a run after finishing the game, usually this involves loading your completed savefile, in Tales of Games for example, you'd keep Artes, Weapons and some other things) Any% = finishing the game, doesn't matter if you get everything or not
Usually you will see "Any% NG" and "Any% NG+", especially on RPGs
More specific stuff that some games might not have :
Low% = finishing the game by getting as few items as possible 100% = finishing the game by getting "everything" (in some games where "100%" is shown on the save file, it just means doing everything necessary to get it, in some other games where there is nothing shown on the save file, it's different, it can be getting all weapons, equipments, unlocking things, etc...)
In some games, 100% can be replaced with other things because of the percentage missing, such as "All Sidequests" (especially for RPGs)
There are a lot more variants depending on what the game is, and what it allows you to do, for example on most Resident Evil games, you would see "Knife Only" wich means finishing the game while only using the knife
Hopefully that helps, if you have more questions though, feel free to ask, and if it's about a specific game, it would be nice for us to know wich one
Pggybacking on previous post, Some additional common categories:
All Levels, All Bosses, All Chapters, or any variant thereof - usually requires unlocking and completing all of the specified content in one playthrough. Common in games as a mid-length category where all of this content isn't required for any%, but doesn't fulfill 100% requirements.
Glitchless/NMG/No Major Glitches - complete the game without using glitches. What is allowed in these categories depends on the game, and minor glitches and exploits are frequently allowed as per the ruleset's definition. Can also be further divided into any%/100%/any other category.
Any% no ACE/no OOB, any other variant - Many games have glitches that allow a game to be beaten in an extremely short amount of time (say, 37 seconds), while banning some but not all glitches can be an interesting speedrun.
112%/152%/200%/etc. - In many games there's a troll % completion, akin to an all achievements run or requiring deathless challenges and/or beating levels multiple times for different badges. In games where there isn't some weird number, but this type of completion is the 100% definition, usually categories such as all collectibles or all levels are more popular.
Partial completion - common in games that are very long or very difficult.
Games frequently also have categories based on things such as the game's difficulty selection or different gameplay modes (for example, assist mode, tokenless mode, easy/hard difficulty, no death mode, etc.), items/characters/powerups used, or co-op gameplay. Meme categories are sometimes played and make it to boards as well.