There is a continental BH grip. Where, assuming the racquet is floating in front of you, ready to be grabbed, and you're looking at the butt end of the racquet like a clock face, your index-finger base-knuckle goes on the 1:30 bevel. This is exactly the same grip as the Hawaiian forehand, turned upside down, and you can use the same face with no change in grip. Just about nobody hits with this forehand.
There is an eastern BH. Here, that base-knuckle is on the ridge (or if you prefer, "wrapped around" the ridge) between the 12:00 and 1:30 bevels. This is the same grip as an "extreme western" FH, upside down. Just about nobody hits with this, either.
There is a "full eastern" BH. Here, the base knuckle is dead on top of the 12:00 bevel. This is the same as a full western FH, upside down. Lots of players use both of these, and thus, the same side of the face. It's highly convenient.
There is an "extreme eastern" or "western" BH. Here, depending on who you talk to, the base knuckle is either on ("wrapped around") the ridge between the 10:30 and 12:00 bevels, or right-smack-on the 10:30 bevel. The wrapped-around version is the same as an "extreme SW" or "mild W" forehand, hit upside down, and the same face is okay for this. The full, knuckle flat on the 10:30 version, is the same as a SW forehand, hit upside down. Even though you could use this one grip, and hit all your groundies with the same racquet face, you'll almost never see it. Since that BH is only for the most extreme topspinny, claycourt fanatics, and that forehand is a good, solid, do-everything FH designed to be versatile in a number of occasions.
(Some sources will call the "Extreme Eastern" BH the one where the knuckle goes on the ridge, and the "Western" the one where it sits flush on the 10:30. This is just a nomenclature issue, and isn't worth worrying about.)