I think this question often depends on the country you live in. BHS is most common in the USA, while flick or flip-flop I've mostly heard used by those in different countries. I live in the USA, so I say BHS.
Same, in ireland we call them back flips!
To me, a flip is entirely in the air, ie. back tuck, front layout, etc.
I actually just call them handsprings... and I will say front handsprings if I don't want them to back tumble.