Sorry, I've never really followed speedrunning, so I apologize if this is obvious.
Essentially, what I'm asking about are speedruns that simply play the game as it was intended to be played (no glitches, proper order / sequence), but quickly.
Usually, the term "glitchless" is used to describe a speedrun that doesn't use any glitches. Glitchless runs aren't very common, since they aren't as fast and require a more in-depth ruleset than glitched runs do. But they do exist. Ocarina of Time, for example, has a glitchless category (with a very strict set of rules defining what qualifies as a glitch and what does not).
Other speedrun categories might ban a specific glitch. For example, in A Link to The Past, there is a particularly game-breaking out-of-bounds glitch, which reduces the speedrun from a little over one hour to a little over one minute. And so, Any% No Out of Bounds is the more popular category. These types of runs are common when there's a particularly game-breaking glitch like this one that makes the speedrun no fun. The terminology for these types of runs depends on the game and the banned glitch.
Back when I was doing speed runs, my friends and I always referred to them as "clean". Where-as a "glitchless" run has 0 glitches or mods being used for the speed-run (look up a lot of emulator speed-runs of old NES and SNES games, so many mods - tool assisted), a "clean" run was following community accepted rules on the game.
Clean, in my opinion, is a better term than glitch-less because there are "glitches" that are accepted by the community, and in many cases (Ocarina of Time) it becomes such a hassle to define what was a "glitch" and what was normal intended game play. For what it's worth, when I tried doing a glitch-less Ocarina of Time run I remember spending more time on the rules than playing, which takes a lot of fun out the the runs.
Speed Run is its own term, not defined in normal dictionaries but Urban Dictionary describes it the best:
In video games. Sometimes Tool Assisted. When a player completes the game as fast as possible, disregarding the environment, difficulty and minor enemies.
Pure -- free of any contamination
Vanilla -- having no special or extra features; ordinary or standard
So I propose the following:
Pure Speed Run -- In Video Games, When a player completes the game as fast as possible disregarding the environment, difficulty and minor enemies without the use of modifications, native glitches or code enhancements.
Vanilla Speed Run -- In Video Games, When a player completes the game as fast as possible disregarding the environment, difficulty and minor enemies without the use of modifications, native glitches or code enhancements.