Mostly called just 'mince pies' here in the UK; rarely made large (like apple pie etc) though, I prefer small ones. They are really nice at Christmas. I usually buy a jar of ready made and add things to it eg, grated apple, orange zest, a little brandy, extra fruit (sultanas etc), until I think it looks and smells delicious. No meat in them, although occasionally there is some suet in homemade and in jars of shop bought mince.
Shop bought small ones to me, are too sweet and have too much filling in them. So, I just add a teaspoon full to the pastry case, top with a smaller circle, or star shape of pastry, or some add a streusel topping, really delicious. Have warm or cold, with or without cream, dusted with icing sugar.
I make a lot, enough to fill a large cake tin, and they last til New Year.