Do you think it is odd to list fish under the heading fish, and shelfish under seafood?

I know several people who for some reason don’t think fish is seafood. I don’t get it.

A few days ago I was at a restaurant and under the entree section one heading was Specialty Fish, and had a bunch of fish dishes listed, and the next heading was Seafood, and a bunch of shellfish dishes were listed. It reminded me of people using seafood to exclusively mean shellfish. I pointed out the menu headings to friends sitting near me at the table, and someone said maybe the fish are not from the sea. But, indeed they were, none seemed to be lake fish.

How do you classify these things. I actually use the term seafood to mean anything from the water, even lakes, maybe that is an inaccurate use of the word? I had not thought about it before. I only differentiate between shellfish and other fish.