What is the (exact) difference between CLM and DIBL in MOSFET?
In my understanding the difference is mainly in the outcome, rather than in cause. In that point of view, they are just different aspects of the same thing.

Channel Length Modulation (CLM) is due to the by the depletion region shortened channel. Higher VDS results in a shorter effective channel.

Drain Induced Barrier Lowering (DIBL): due to the by the depletion region shortenend channel, there are fewer mobile charge carriers, hence a smaller gate voltage is enough to balance their electric field. The higher VDS is, the lower Vth become.