An object may have–

At any instant, speed = magnitude of velocity.

So, if speed varies, velocity also varies. In case of uniform circular motion, particle's speed remains constant but velocity varies because of change in direction. If velocity does not vary then acceleration $=\overrightarrow{a}=\frac{d\overrightarrow{v}}{dt}=0.$

If speed does not vary but direction of motion varies then velocity varies hence acceleration will be non-zero.