The most common is "Any %," also the most basic, it means finish the game, usually anything goes, glitch away.
You can also have no glitches category, 100% complete, no warps, no powerups, all <game item>s, etc. Sky's the limit. The community creates the categories.
There is, however, OoT Randomizer[1] which is really fun to play and watch. You can get end stage items at the beginning depending on your seed.
Over the years the Super Mario Bros community in particular has become more accepting of glitches, as otherwise both TAS and human runs would have hit the limit of how fast is possible. By allowing glitches there is now always a possibility that the runs can be further improved.
Indeed, which is why I said "usually."
I usually see "Any %" and "Any % no glitches," but I just dabble in watching speedruns. If I see "Any %" with no other qualifiers, I'm going to assume glitching is allowed.
I think it can be a bit arbitrary at times when a technique is considered "glitching" or not. The community decides. Which is fine.
I saw a speedrun of Super Ghouls and Ghosts that had a clever limitation - "pick up all weapons that show up." If you're familiar with the game, if you pick up a weapon you lose your previous weapon and some weapons are way worse than others.