aside from ‘old’ design like angular or Scythian’s… I tend to agree on how Gao-Ying classified ‘modern’ composite-bow on just two basic categories, Da-Shao-Gong (long-ear bow) and Xia-Shao-Gong (small-ear bow)… variations of both might be great according to local tradition, but the fundamental structure of the two is distinguishable from each…
example of long-ear bow: Hunnic, Magyar, MB, Tang, Seljuk, Mongol, Manchu, Mughal, etc…
example of small-ear bow: Mamluk, Ottoman, Korean, Chahar-Kham, Persian, etc
There’s also a lot of variation within reach of those"categories" depending on the date of manufacture, purpose of the bow and individual preferences of bowyer and archer.
For the older types, complete bow find are so rare, it’s hard to make hard and clear definitions. Since each bow was individually hand made as it’s own thing, categorization will always be a bit artificial.