Is this game mission based (a la TIE Fighter or Wing Commander) or open "water" (a la Privateer/Elite)?

Somewhat, though it's more of a simulator andt has a lot of emphasis on using stealth so there is not as much action.
It's no openworld game like Elite and there is no trading.

If you fancy a straight up underwater Wing Commander clone I recommend you take a look at Archimedean Dynasty