What do you call the equivalent of "Cardinal directions" in a hex-grid?

In a square grid, the concept of "Cardinal Directions" refers to the set of directional vectors {[0,+1],[0,-1],[+1,0][-1,0]}, aka EAST, WEST, NORTH, and SOUTH.

In a hexagonal grid, the equivalent set (that is, directions along the intuitive 'major' lines), depends on the orientation of the hexagons. For pointy-tipped hexagons (what I'm using), in axial co-ordinates it's {[+1,0],[0,-1],[-1,0],[0,+1],[-1,+1],[+1,-1]}, aka WEST, EAST, NORTHWEST, SOUTHEAST, SOUTHWEST, and NORTHEAST.

What would you call this set?

Alternatively, "the six directions"

There simply isn't enough ambiguity in relevant directions on a hex map to need more specificity than that, or at least not often enough that a specific term has gained general use.

For that matter, I rarely see "cardinal directions" in board games either - "orthagonal" (and "diagonal") are much more common.

Unless your game is very strongly real-world inspired, i.e using historical maps as layout, I'd consider it a metric with six cardinal directions, state it at the very beginning and go with it.

If I am moving on either a square grid, or in normal (Newtonian 3D) space, the four cardinal directions make sense (plus the two vertical ones, for normal space). (There are exceptions: some societies have "ahead/behind" and "towards/away from the river", for instance. Hell, in Pittsburgh we sometimes use "up/downriver" and "towards/away from the river"!) Additionally, they are orthogonal, which is a huge advantage.

Are you asking from the POV of the PCs/game tokens, who (presumably) don't see the hexagonal grid projected onto their world? They'd likely still use cardinal directions.

Or are you asking from the POV of the players? Moving one square northwest makes sense, but these are really not "directions" when one moves two or more squares. "One west and then one northwest" is klugey. OTOH, "North by northwest", "168 degrees", or "22 degrees west of north" all are real-world examples.

If you're only asking about the player POV of one-unit moves, then the set "W, NW, NE, E, SE, SW" would seem to make sense.