If a car moves with constant velocity, does it also move with a constant speed?

Yes. The fact that an object moves at constant velocity implies that its speed is also constant. Note that the converse statement isn't necessarily true.

Explanation:

Velocity is a vector. For two vectors to be equal to each other,

In motions, the magnitude of an object's velocity is the same as its speed.

If the car moves with a constant velocity, that means that

In other words,

.

Note that the arrow here points only from the velocity side to the speed side. It doesn't point backward because knowing that the speed of an object is constant won't be sufficient to prove that the velocity of the object is also constant. For example, for an object in a uniform circular motion, the speed is constant but the direction keeps changing. Hence the velocity isn't constant.