Pretty much sums it up. Wrestling is a subset of rules within grappling which favours takedowns, control and pins, while grappling overall encompasses takedowns, throws, pins, submissions, sweeps etc and can be done in a gi or in no gi.
Wrestlers wear onesies. Submission grapplers where board shorts and a skin. BJJ guys wear gi's or a skin and board shorts.
Those are the three predominant forms of grappling used in MMA circles but there are also a wide variety of different rulesets and arts. Judo. Aikido, TJJ/JJJ, Chidoaba and Turkish oil wrestling (a real sport where the competitors wear leather pants, cover themselves in olive oil and wrestle with the primary objective of the match being to stuff you hand down the other guys leather pants. I am not kidding. Real Sport)