The difference between terrestrials and non-terrestrials is simple: terrestrials inhabit planets whereas non-terrestrials inhabit outer space.  There are not several different species of ‘aliens’ running amok on Earth.  There are not different ‘species’ of ‘aliens’ who have different planetary origins.

The situation is more simple than you think it is.  The entities whom you regard as ‘aliens’ are all ‘non-terrestrials’, in as much as none of them inhabit ‘terra firma’.  Humans are terrestrial beings, we inhabit ‘terra firma’.  We are not the only terrestrials in the Universe, there are others.  Terrestrials do not leave their terra firma and embark on space travel to occupy the terra firma of other terrestrials.