Zero acceleration means "no change in velocity" or constant velocity. Does not mean zero, just means not changing with time (or at this instant). It can be zero, it is just not required to be any particular value or sign.
Zero velocity means it is at rest. It might be accelerating, and is "at rest at this instant".
A boy holds his arm out at shoulder level, with a ball in his hand, palm facing down. The boy releases the ball...
- Just before release, acceleration and velocity are zero.
- At the instant of release, the ball has non-zero acceleration, but zero velocity.
- Some time later, but before the ball hits the ground, it has the same non-zero acceleration (on small scales, that is how gravity works), but non-zero velocity.