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I suggest the following terminology for certain categories of chess pieces.
Runner pieces move like rider pieces, except that they can only capture on the first move in the series. An example of this is the Kwagga, which moves like a Camelrider, except that it can only capture on the first leap. This means that the Kwagga could also be called a Camelrunner. Another example would be the Wazir. If we allow the Wazir to move like a rook, but still only capture like a Wazir, then it's a Wazir-runner (remains to be invented, I suppose). In fact, the rook could also be called Wazir-rider.
Transformational pieces are pieces that change capacities depending on square colour, or row number, for instance. An example of this is the Elkrider.
Telekinetic pieces are pieces that can dislocate other pieces by moving towards them or from them. An example of this is the Echidna.
Catapult pieces are pieces that dislocate other pieces by hurling them over its head in the movement direction. An example of this is the Belfry.
Agglomerate pieces are pieces that combine two movement types (i.e. two pieces), but they move only with the one movement type, whereas they capture only with the other movement type. An example of this is the Constable. Agglomerate means 'clustered together but not coherent', which is a term that separates this piece type from the compound pieces.
Compound pieces simply combine two or more pieces. An example is the Amazon, which combines knight and queen.
Bifurcation pieces change movement from diagonal to orthogonal, or vice versa. An example of this is the Secutor.

These terms can be combined in order to categorize new pieces. For instance, it's fully possible to create an agglomerate transformational piece, or an agglomerate catapult piece. /Mats