Marine is a broad term referring to anything related to the sea or ocean—organisms (marine fish, mammals), activities (marine navigation), and phenomena (marine climate, pollution).
Ocean specifically denotes the five vast saltwater bodies covering most of Earth: Pacific, Atlantic, Indian, Arctic, and Southern Oceans. They are characterized by immense size, high salinity, and climate regulation roles.
In short, "marine" encompasses all sea-related matters, while "ocean" names the specific large water bodies.