May I ask what in the hell is the difference between this thing and that thing?

I'm probably gonna get this wrong, but

• Remix - well, remixing aka changing how the original sounds;
• Cover/remake - doing the replica of the original as accurate as possible.

Here you're choosing whatever thing your work is closer to.

in other words:

remix = rearrange sound order (Beethoven's 9th symphony, but the most famous bit is in the beginning of the track instead of somewhere in the middle and/or repeats itself throughout the track)

cover/remake = same sound order but different instrument/style (guitar solo/8-bit version of Beethoven's 9th symphony)