My Kenneth Katzner dictionary translates grasshopper only as "кузнечик". And if you look up in virtually any internet dictionary, it is still "кузнечик". No more, no less.
However, I recently found that there exists a bug called katydid. Katydids have a green body, very long antennae, and if I do not mistake, they make their sounds using their wings rather than their hind legs.
Thus I have been confused. Katydid = кузнечик? Then how do you translate "grasshopper"? I'd appreciate more information about this issue.