By "top down", do you mean 3/4 view, like in many RPGs and Hyper Light Drifter? In true top down, there'd be no difference in sprites facing different directions, they'd just be rotations of the same sprite - we'd just see the top of the head, the shoulders, and maybe parts of the legs when the character walks.
Hyper Light Drifter seems to have at least 4-directional idle and movement sprites (with mirroring, that's 3 sets of sprites - facing north, south, and east/west):
The "slanted orientation" is just diagonally positioned sprites. Isometric games have these as their default or only sprite types, since they usually limit motion to northeast/northwest and southeast/southwest:
I'm not sure, but attacking in HLD might have only two sets of animations, like you said - northeast/northwest and southeast/southwest. I've seen a few games do this, I suspect it's because players are less likely to notice the attack animations being less flexible since they're focusing on not dying while they're in combat, and because it allows for more consistent attack hitboxes.
For non-attacking movement, if you're going to have 4-directional (or more) movement, I recommend having 4 directions (3 distinct animations) for your sprites because having just two would be pretty noticeable. It seems easier to get away with diagonal movement reusing north, south, and east/west animations than it is to get away with cardinal movement that uses diagonally-moving sprites.