Is There an Equivalent Concept to American Vs. European Exercise in Cryptocurrency Derivatives?

Yes, the concept is present in some crypto derivatives. While most standard crypto futures are European-style (settled at expiration), crypto options often follow the American or European distinction regarding exercise.

Furthermore, perpetual swaps, which are unique to crypto, are a form of derivative with no expiration, making them an infinite-term contract, a different class altogether. The exercise style dictates the flexibility of the contract holder.