Brazilian 
Brazilian waxing includes the removal of ‘all’ hair in the pelvic area from the front to back. 

American 
A basic bikini wax, the removal of only the hair that is exposed by a ‘modest’ swimsuit or panty. For a bikini, it would be hair at the top of the thighs and under the navel.

French
A French Bikini is not as conservative as an American and not as invasive as a Full Brazillian wax. It will include the additional removal of hair off the top/directly under the bikini line, under the crease line and a little more off the sides/inside the bikini line.