Well technically you do take the thread pitch into account for all items.
As course, fine, and fine-fine just points to the agreed standard for that diameter.
I.e. a M4 metric course would be 0.7, fine would be 0.5 and fine-fine would be a custom spec product
whereas an M12 metric course would be 1.75, fine would be 1.5, fine-fine 1.25 and super-fine 1
But when asking for a M4x whatever product, one assumes that the user means standard thread, or that thread pitch is irrelevant so long as nuts are provided with the same thread.
But most things are defined within the DIN specification for the particular product
e.g.
Socket cap = DIN 912
Socket button = DIN 7380
Set screw = DIN 933
Bolt = DIN 931
Hex nut = DIN 934
etc, etc
trust the Germans to have a better way of doing things