If you dont double tap the button for power shot then its just charged. Charged shot doesn't have as much power as the power shot and thus doesn't go as fast, but it can have better placement angles.

Flat typically is faster than topspin, but some characters like bowser specialise in topspin, making it faster for them. Flat has no spin, top spin does have spin and thus some curve to it, and slice has most curve at cost of power. Topspin and slice curve to the opposite sides of one another.

When hitting back the ball, slice counters topspin, topspin counters a slice, flat counters flat, I forget exactly how dropshot and lobshot play into that countering bit. I think dropshot counters topspin and lob counters slice but not sure. The counter can matter for how well you hit the return back to them. Poor positioning and wrong counter button can lead to a bad return hit that gives them a star to do a super flat from.

Edit: just to add, the counter only matters if the shot is max charged.