What is the standard practice for animating motion — move character or not move character?

I’ve downloaded a bunch of (free) 3d warriors with animations. I’ve noticed for about 25% of them, the ‘run’ animation physically moves the character forward in the z direction. For the other 75%, the animation just loops with the characters feet moving etc., but does so in place, without changing the character’s physical location.

I could fix this by:
1.) Manually updating the transform in code for this 75%, to physically move the character
2.) Alter the animation by re-recording it, with a positive z value at the end (when I did this it caused the character to shift really far away the rest of the units, probably something to do with local space vs world space I haven’t figured out yet).

But before I go too far down this rabbit hole, I wonder if there is any kind of standard? In the general case, are ‘run’ / ‘walk’ animations supposed to move the character themselves, or is it up to the coder to manually update the transform while the legs move and arms swing in place? Is one approach objectively better than the other, or maybe it depends on the use case? If so, what are the drawbacks of each? I know nothing about animation, so I don’t want to break convention (if there is one).