What is the difference between negative acceleration and retardation?

Negative acceleration just means acceleration in the negative direction. It doesnt tell us whether the speed is increasing or not.
 eg:- suppose i am throwing a stone upward with a velocity v. Now let us study the up and down motion of this stone. The initial velocity is v(up direction) and let it be positive. Now here acceleration is g which is negative because g is always acting downwards. Now in the downward motion velocity becomes negative(since direction of velocity acts downwards), g remains negative(as g is always acting downwards). But here the velocity of stone keeps increasing though the acceleration is negative. So it is clear that acceleration is negative doesnt imply that speed is decreasing.

I hope the point is clear

Retardation is the acceleration in the negative direction of time axis ie. opposite to the motion. Decreasing accleretion is the decrease in the magnitude of time rate of change of velocity.