Standard Bikini: This wax will remove the hair that will fall out of a standard pair of underwear - Think upper inner thighs and just slightly more inward. Often clients will ask me to wax the top part of the pubic hair down half an inch or so just to make it look a little more shapely.
French Bikini: A french bikini is most delicately described as removing the hair that would fall outside of a pair of thong underwear. This wax style removes more of the pubic hair inward and from the top but does not encroach on the labia. It does, however, remove the hair around the anus.
Brazilian Bikini: In the most basic terms a brazilian wax is EVERYTHING. You can request a strip or a small triangle at the top of the pubis bone but the notable feature (and where the important skill set comes into play!) is that a brazilian removes the hair from your labia and around the anus.
Pro Tip: Your anus has very few nerve endings and as a result has a relatively small amount of sensitivity to hair removal. The most nerve endings are located at the top of the pubis bone (think where the "landing strip" reaches its lowest point). Coupled with the fact that most women have a dense growth of hair this is usually the most sensitive area.