Both characters were created for The Great Santa Clause Switch, where they were known as Frackles. Gonzo was called Cigar Box Frackle in that special but also went by the name Snarl in a song, and Droop was called P.J. Dripsnout in the design sketches but was referred to in a song as Snivelly.
After that special, their names and personalities were changed. Droop's eyes also changed from angry-looking eyes to sadder eyes, and his feet were removed.
I think Gonzo's species was meant to be ambiguous. There have been many instances where other characters (including Gonzo) mention that they don't know what he is. Starting with The Great Muppet Caper, he has often been referred to as a Whatever. On Muppet Babies he is frequently called a weirdo.
In Muppets From Space, Gonzo learned that he comes from outer space. Of course, the name of his species is never actually mentioned (is he an alien? a martian?)