Question

Difference between normal and tangential acceleration

Answer 1

When an object moves in a circle, it has a centripetal acceleration , directed toward the center. We know that centripetal acceleration(ac) is given by ac=v^2/r. This centripetal acceleration is directed along a radius so it may also be called the radial acceleration.

If the speed is not constant, then there is also a tangential acceleration (at). The tangential acceleration is, indeed, tangent to the path of the particle's motion.

Answer 2

Tangential acceleration is the one that is related to the centrifuge force, which means it appears when you have a rotational movement. The direction of a tangential acceleration is oriented to the center of the rotation movement. Tangential acceleration doesn't make the object move faster, since it is always at a 90 degree relatively to the velocity vector. 
A normal acceleration is anything else, like a car or a train.