On the European side of the Atlantic, Laura, a pie can be savoury or sweet. A meat pie would usually be with beef, but equally could be with lamb - but you'd rarely see something advertised as simply a 'meat pie'. You can have a steak and kidney pie, a beef and onion pie, a lamb and gravy pie, a chicken and mushroom pie, and so on. These can be large (serves 3-4) or individual. If you visit a fish and chip shop in the UK, an alternative to fish is a pie.
And, yes, of course we also have apple, cherry, rhubarb, blackberry and so on pies.
A 'pot pie', however, means nothing to us and sounds weird. I really did think that it was made in a saucepan! (Which reminds me: I still haven't figured out what a 'pot roast' is...)
Oh, and one further addition on 'pies': shepherd's and cottage pies are completely different. No pastry; they're covered in mashed potato, which can be cheesy or not. One is made with minced (US: ground) beef, the other with lamb. And I can never remember which is which!
I really did think that it was made in a saucepan! (Which reminds me: I still haven't figured out what a 'pot roast' is...)
