The first recorded use of the term "Welsh rabbit" was in 1725; the first recorded use of the term "Welsh rarebit" was in 1785, in Francis Grose's book A Classical Dictionary of the Vulgar Tongue. The assumption by Grose is that "rarebit" is a corruption of the word "rabbit".
The origin of the initial "rabbit" term is also obscure. There is a theory that "Welsh rabbit" was a reference to the idea that Welsh people were too poor to afford meat, so they ate cheese instead.
There are many variations: English rabbit, Irish rabbit, Scotch rabbit, etc. When topped with a poached egg it's called a "golden buck".
The word "rarebit" seems to exist solely as a variant of "rabbit", for this dish alone.
