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I wanted to know how many penhold grip types are there

Three types
1. TAG (Traditional Asian Grip) or just TPH(Traditional Asian) :- This is the older style of play using penhold grip where the player uses only one side of the racket on both forehand & backhand. Ther is rubber only on one side of the racket & other side has a paint sheet.
2. RAG (Reverse Asian Grip) or just RPH(Reverse Asian) :- This is the newer style of play using penhold grip where the player uses both sides of the racket just like a shakehand player. There is rubber on both sides of the racket
3. HAG (Hybrid Asian Grip) or just HPH(Hybrid PenHold) :- This is the newer style of play using penhold grip where the player uses both sides of the racket just like a shakehand player. There is rubber on both sides of the racket & the player uses both TPH & RPH strokes

Please note that Asian grip is also called the vertical grip in China
And the shakehand grip is called the horizontal grip in China

TAG :- Quite a few former world champions used TPH using wide or stiff pips (with sponge). Some used spinny inverted rubber.
HPG :- First player & probably the only world champion who used hybrid penhold was Liu Guo Liang . He had wide or stiff pips on the forehand and used both TAH & RAH with it . He also used a spinny inverted rubber on his backhand to loop. He also occasionally twiddled his racket at critical junctures in a match. This is probably the best style of penhold. 2024 USA National Women's Champion Hong Lin also uses this grip

RAG :- These players mostly use spinny inverted on both sides of the racket & loop from both sides. They do not play TAG on their backhand side using forehand rubber. Xu Xin & Wang Hao are the best examples.

There is also another older method of classifying penhold grip types before the arrival of HAG & RAG when
there just was only TAG
But this classification is still used but it is more about the shape of the racket & how it is held in one's hand rather than the playing method used as in TAG, RAG & HAG

Japanese Penhold (or jPen) & Korean Penhold (or kPen) :- kPen & jPen are quiet similar & the notation kPen is rarely used. This is mostly because Chinese arrived on the TT scene as successful in 1959 and Japanese followed in 60s. Korean successes came in the 80s and after.
Most jPen (or kPen) rackets are rectangular in shape

Chinese Penhold (or cPen) : Most cPen rackets are oval or circular in shape.