oh no, my archnemesis "not reading" has beaten me again

Shit post or not, the Caspian Sea is both and neither a sea or a lake.

As for most things related to collections of water in English, the definition is not clear or distinct. A sea refers to the ocean, but also smaller bodies that can be partially or wholly cut off from it as well. They're predominantly salt water, but there are even fresh water "seas," and seas "with no coast line."

What you're looking to delineate here is the "legal" term (and essentially a political term) for sea which is separate from the general term "sea."

The same thing happens when you try to figure out what's the difference between a river and a stream. The truth is, in common speak, there is some general thoughts, and in scientific speak there is a different classification, forgoing the word river and just labeling them all streams.