A lot of decapods exhibit heterochely (the claws are formally “chelae” and the legs (“pereopods”) that bear them “chelipeds”). In some taxa, handedness isn’t even consistent within the same species.

There’s a popular focus on heterochely arising because of different food types, but there are nuances. For example, this is often quite different between males and females.

In addition to just being different in size (allometrically), they’re often also different morphologically (in shape). For example, for crabs who prey on bivalves, one claw may be more suited to crushing while the other is more suited to handling, rapid movement, cutting, etc. So it’s not just about how big they are as described in the OP.

There’s often also a major element of sexual selection (Mr. Krabs wasn’t lying), and other major uses of claws depending on species are competition (getting into fights) and burrowing.

Etc.