
It may not make sense to call both series Final Fantasy now, but back when these were released, RPGs were not as popular as they are today and nobody was very knowledgeable about Japanese series, so I'm sure calling them both Final Fantasy for name recognition in the US seemed like a good idea at the time.
Yeah that first moogle battle can be tough. You can either cheese it and have only one team do all the battles, or let the other teams be damage sponges while you have the team with either Locke or Mog in them do the bast attacks on the boss. Later on you'll have to do a more complicated version of those 'strategy' battles but there it's best to make a good team and have just them fight all the battles.
I finished the main story in Lil' Gator Game but I didn't do anything after that. Cute game for what it is, though.