[willseth]

Depends on the instrument. For wind instruments, the motions basically don’t change, and your focus is on synchronizing your mouth with your hands. Tonguing technique is different at high speed but you would typically practice with the same technique at low speed when learning a fast piece.

[ses1984]

But the motions do change, at very slow tempos you can move basically one finger at a time, at faster tempos you have simultaneously overlapping motions.

[willseth]

On a trumpet? A clarinet? No, the motions don't simultaneously overlap. The fingering mechanics are slightly different at speed, but you would still start slow while using the higher speed mechanics and tonguing technique, not jump into high speed practice first.