Though, I don't share your optimism - I sure appreciate your mind expanding terminology. What might these other "non-terran" environments be?...space?...gaseous planets or some such?
"non-terran" simply means "not (of) Earth"
"non-terrestrial" means "not LIKE Earth"
I seriously doubt that we'd be able to recognize life which developed on a non-terrestrial world, even assuming we ever manage the trick of expanding out of this puny little system.