Not a marine vet but I work with several in the fish farming sector in the UK (I'm a marine biologist and fish health manager). In the UK there are certain things that require a vet sign off like attestations for any fish products being exported, they also control any medications including issuing prescriptions for anaesthetics that are essential for checking live fish. They do a mix of site routine visits, health diagnostic visits for serious or unknown issues, including collection and preparation of lab samples. A lot of it is regulatory work with a lot of paperwork, or contracted services where they will work with lab diagnostics and provide a support function or third party verification, could also be inspection of premises and vessels associated with fish handling. There is no difference in veterinary degrees, they haven't done a specific aquatic veterinary degree but have branched into aquaculture at some point in their career.

A couple I know have previously worked for certification bodies for example ones that introduce welfare standards or for government services that regulate fish farming. A couple do service zoos and aquariums but it's usually on a consultancy basis and not full time.

The aquatic species can mostly be managed with little medication etc so you see more roles like mine where you can diagnose and manage things with little direct veterinary requirements. Obviously large marine mammals would be different but I don't know if anyone with a full time career in this field.