Many times, when my sensei teaches me a technique, he takes reference from either wrestling or grappling. I always thought the two are different terms for the same art until the master told me that it's not the case and wrestling is different grappling. But, I still couldn't understand the difference between the two. Can someone help me understand it clearly.
Quite frankly, there is no objective difference between the two, so it's more likely simply a distinction created by your teacher. Most likely, he's differentiating between Western techniques one might see in amateur Greco-Roman wrestling, and grappling techniques seen in something like Brazilian Jujitsu.
Grappling is a more generic, umbrella term than wrestling. Striking from a Muay Thai clinch, for example, is part grappling but not wrestling.
Standard disclaimers apply, however, that people use words differently and in ways that disagree.