The terms "Alpha" and "Omega" (roughly meaning "first" resp. "final") are blurry in-universe terms used by some writers to categorise different characters. Omega mutants are, in theory, supposed to be the most powerful class of mutants, but with time the scope of the term has widened to include a much wider scope of characters that, following the same logic, could technically qualify half the ones in existence.
Originally omega mutants were beings with vast control over matter and energy, such as Iceman, Phoenix, Legion.
The term "Alpha mutant" can, but does not necessarily, intersect, but the distinction is usually blurry, and varies depending on the writer. Jean Grey is sometimes considered an "Alpha" because of her type of power, and lack of flaws, whereas Gambit is sometimes also considered as an alpha, but not as powerful enough to be an "Omega" in his normal state. However like Jean Grey, his powers where held back since he was unable to control them, when he gets all of his powers back he becomes the most powerful hero in all of the Marvel universe.