velocity can not be constant if the acceleration is not zero.
speed can be constant even if the acceleration is not zero.
By definition acceleration is the amount of change in the velocity per unit of time. It follow that if the acceleration is zero, the amount of change in the velocity must also be zero.
acceleration (and velocity) both contain a directional component; a change in direction is one form of acceleration.
speed is independent of direction; a change in direction does not necessarily mean that there will be a change in speed; a typical example of this is the rotation of one body around another body; the speed may be constant although the direction is constantly changing (and thus the first body is constantly accelerating).