I'm just confused on what's the between Any% and No Warp Speedruns. While I do see that "Wall Run Warps" Change the Category, what does it mean exactly and how does that change the category?

It changes the categories because it can be done in Glyphic Canyon, and is really stupid to pull off, so it affects every category in a very unfun way. Most people running Shadow probably won't want to do Any%, but still want to do runs with Chaos Control Glitch, so the new Any% was born.

On Gamecube versions of the game, if you wall run into certain areas of levels where the wall is sticking out a tiny bit, you can cause Shadow to warp incredible distances. You can see this in some of the ILs for Glyphic Canyon, Sky Troops, Air Fleet, and Lava Shelter.