Collision versus force: is there a difference?

Generally, a force is only going to keep the velocity magnitude of the target body constant, if the transferred momentum is infinitely small. This is actually a slightly convoluted way of saying: the force that is perpendicular to the body's velocity is generally going to keep the velocity magnitude constant only in a single moment. You can't generally assume that the force is also staying perpendicular "one moment later" (because at least the direction of velocity itself has already changed), and therefore, you can't assume that the velocity magnitude is staying constant over a prolonged duration. An important case where this assumption is actually true, however, is of course the Lorentz force on a charged particle in the magnetic field.

What happens during a perpendicular impact is that a finite amount of momentum is transferred to the target body, which violates the introductory condition. Actually any impact has a finite duration, during which initially perpendicular force and velocity can change to non-perpendicular: $$Delta vec p = int vec F dt$$ Just as an example: if the force $vec F$ is assumed to be constant (which will usually not be the case during an impact, but it is easier to calculate), then (P=mechanical power) $$frac{dP}{dt}=frac{d}{dt}(vec Fcdot vec v)=vec Fcdotfrac{dvec v}{dt}=frac{1}{m}vec F^2>0$$ Thus, even if initially $P=vec Fcdot v=0$ due to perpendicularity, in the next moment will be $P>0$ (because velocity magnitude of the target body increases).