I've always said prawns for everything, small prawns for small ones all the way up to tiger prawns. I seem to remember my aunt calling the small ones shrimps, so that might have been common. Prawn cocktails always seem to have very small prawns, so I suspect we in Britain stopped calling them shrimps at some stage.

I now shop at Costco, and I looked today - there seems to be a real mixture, according to country of origin/intended market, very little to do with size.