It's entirely parallel to woodworking jargon, even directly derived from picture framing and casement window moulding terminology via analogous contact printing frame design. A common shoulder plane was termed a rebate plane if made in Britain, such as olden British Stanley, but was termed a rabbet plane if made in the US by Stanley-Bailey, even during the same era (now Stanley is almost entirely made in China, and is best characterized as a Junk plane instead). I imported a lot of that kind of stuff from a variety of makers. The Germans like Kunz had their own term, but labeled them Rabbet planes when packaged for US sales. And there was a midwestern maker of tiny offset planes for sake of instrument makers who cutely marketed them as "Bunny Planes" - little rabbits. If those were made in the UK instead, they'd probably be termed Hobbit Hares.
When I used to write articles for Fine Homebuilding, they'd create sidebars to iron out contradictions in terminology even between East Coast and West Coast tradesmen, plus the general public - even had separate East Coast and West Coast editors. The Western one lived up there at Sea Ranch. Since I was heavily involved in restoration consultations, the local terms were very well established well back into the 19th C. If Carleton Watkins or Muybridge had asked a SF cabinet maker to make a contact printing frame for them, the term rabbet would have come into play. And I don't think it was derived from the "ribbet" of a Calaveras Jumping Frog that Mark Twain wrote about. Cottontail rabbits themselves don't talk much, so I don't know their own opinion on the subject.
