Tangential and angular acceleration are two different ways of expressing the same thing - that the object is going around the circle slower or faster. The tangential acceleration is equal to the radius times the angular acceleration.
Centripetal acceleration is what keeps the motion circular - without it, the object would go in a straight line. There is an equation that relates it to the angular (or tangential) velocity.
The only force acting on a satellite in a circular orbit is gravity, which is toward the Earth, so the satellite has only centripetal acceleration. It goes around the Earth at a constant speed, so the tangential acceleration is zero.
If the satellite fires its rockets, it can have tangential acceleration for a time.
Hope this helps. Post again if you have any questions.