What is “geometric algebra”, and what has it been in historiography?

Much ink has been spilled these last 50 years over the notion (or whatever it is) of “geometric algebra” – sometimes in disputes so hot that one would believe it to be blood.
However, nobody has seemed too interested in analyzing whether others have used the words in the same way as he has himself (he, indeed – as a feminist might declare, “all males, of course”). So, let us analyze what concepts or notions have been referred to by the two words in combination – if any.