Honestly, grip definitions differ from player to player. When I started, all I knew of were continental (and it's many variants), mild eastern (knuckle on the edge of eastern and continental), eastern (top bevel), and western (1 bevel beyond top bevel).
Now, I hear mild eastern was eastern all along, eastern was full eastern or even western, and hardly anyone knows western because few people have ever gone that far deep (Shroud, Kuerten, and Henin are the only ones I know that use it).
But back on topic,
"Strong" Continental backhand (holding continental like a hammer almost, hard to describe; palm should be mostly on top bevel rather than the same slant the knuckle is on) -> Eastern forehand (index knuckle on side bevel) : Generates primarily flat shots, but has good access to spin when wanted or needed.
Mild Eastern backhand (index knuckle on slant past continental) -> "Strong" Eastern forehand (index knuckle on edge below side bevel) : Slightly better access to spin while retaining ability to hit flat, the most flexible grip. Notable users were Edberg, Lendl, and Dimitrov.
Full Eastern backhand (index knuckle on top bevel) -> Semi-Western forehand (index knuckle on bottom slant bevel) : Exceedingly strong baseline grips, excels in exchanging heavy topspin groundstrokes while still capable of hitting flat with good mechanics, but suffers slightly on wide balls due to most users of these grips having contact points farther in front (but people either run fast enough to make this irrelevant or know how to hit a good sliced or flat lob with a continental grip). Notable users are Federer and Wawrinka.
"Strong" Eastern backhand (index knuckle on slant past top bevel?) -> "Strong" Semi-Western forehand (index knuckle on far edge of Semi-Western) : Access to loads of topspin, slightly harder to flatten the ball out, and issues with low and wide balls become even more noticeable. The only one I can immediately think of that uses this grip is Gasquet. I initially believed Wawrinka hit with this grip as well due to the way he hits the ball and how heavy he can hit it, but he uses a mild eastern.
Western backhand (Semi-Western forehand flipped over) -> Western forehand (index knuckle on bottom bevel) : Access to loads of topspin and prefers almost exclusively deal with heavy topspin due to very noticeable issues with low balls (and wide balls) and ease with dealing with high balls (also, good luck ever generating a flat ball). Shroud, Kuerten, and Henin are the most well-known users.
Most people fall into continental and mild eastern. That's where probably more than 90% of OHBH users fall. The remaining 9.99% use full eastern or strong eastern. The masochists and clay lovers make up the remaining western grip.
