For me, a pie is something savoury or sweet fully enclosed in non puff pastry.
A dish being cooked and eaten from an individually served bowl or a large one which is served as potions with just a pastry lid I don't think of as a proper pie, that's just an upside down tart/flan.
Cornish pasties, made with puff pastry; I consider savoury pastries.
IIRC Cornish pasties were originally made with harder pastry, like pies. Legend/Myth (maybe true) was that the pastry joint was held in miners hands, which were dirty and discarded.