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I don't know, is it ok, but here how i see this:
Directions:
Orthogonal;
Diagonal;
Diagonal+orthogonal;
Divergent - captures diagonal, moves orthogonal;
Captures orthogonal, moves diagonal;
Forward-only orthogonal (it don't mean sideways);
Forward-only diagonal;
Forward-only diagonal+orthogonal;
Captures forward diagonal, moves forward orthogonal;
Captures forard orthogonal, moves forward diagonal;
Gold - orthogonal+forward diagonal;
Silver - diagonal+forward orthogonal;
Captures as gold, moves as silver;
Captures as silver, moves as gold;
Are reverse gold and silver (and thier divergent versions) worth?
Dragon king - orthogonal is long-range, diagonal is short-range (see below for range);
Dragon horse - diagonal is long-range, orthogonal is short-range;
Capture as dragon king moves as dragon horse;
Moves as dragon king, captures as dragon horse;
Forward-only versions of dragon anddivergent dragon pieces.
Hopping (cannon-like moves. It's only possible to hop over pieces on spaces, where hopping piece would be able to move if it would be non-hopping move):
Non-hopping;
Chinese - moves as non-hopping, captures as hopping;
Korean - both captures and moves are hopping;
Moves as hopping, captures as non-hopping.
Range:
Long-range;
Short range (hopping short-range pieces leaps to closest space, where respective long-range would be able to move, that is, hopping version of man is grasshopper, hopping version of ferz is bishopper, etc.).
Kinds of movement:
1 step - ferz, wazir, ferzrider (bishop), wazirrider (rook), etc;
2 steps - alfil, dababah, alfilrider, etc;
1 step move, followed by another 1 step move at 45 degrres;
1 step move, followed by 2 step move at 45 degrees (zebra, Korean elephant...);
2 step move, followed by 1 step move at 45 degrees (camel);
2 step move, followed by another 2 step move at 45 degrees.
Originally i thought about bent-riders (like gryphon) as long-range versions of bent movers, but now i think nightrider-like pieces are better.
Leap ability:
For 2-step movers it's simple: leaping and non-leaping (how elephant of shatranj differs from elephant of xiangqi);
For bent-movers, there are 3 groups:
Each bent move is unblockable at all (that's how FIDE knight and zebramoves);
Korean elephant-like: alfil and dababa moves are non-leaping;
Alfil and dababa moves are unblockable, but move can be blocked when piece turns 45 degrees (this version of zebra and Korean elephant makes 1 wazir move if square is empty, when turns 45 degrees and makes leaping alfil move. Non-leaping knight of this group don't differ from non-leaping knight of previous grop, but camel, zebra and (4,2) mover are different).

There are already too many pieces. Other suggestions?