What is the difference between an equalizer and a channel estimator?
In communication systems, transmitted signals are distorted by the physical medium (the channel) charactheristics.

The channel estimator tries to identify the transmission channel characteristics, by computing (estimating) various of its model parameters.

Then, the channel equalizer tries to restore to distorted (received) signals back into their originals via some sort of inverse filtering (equalization) on the received signals, which was designed according to the estimated channel parameters.

Both operations are approximate; depending on the application, they can be very effective or not so.