I'm with your mum, mostly, except that I think of pies (meat or apple etc, pastry lid) as being large, to feed several, and tarts (open, always sweet) as small, individual. Flans, open, always sweet, sometimes made with sponge rather than pastry, large. Quiche, open, always savoury (eggy filling), usually large, small defined specifically as mini-quiche and a modern innovation.