What are you talking about?
It was always assumed that vaccinia was a variant of cowpox, but genome sequencing studies of poxviruses during the last few years have shown that it's not:
Originally, "vaccinia" was propagated from one human arm to the next, keeping the strain going.
In 1845, it was shown that the virus could be propagated in cows and the vaccine was then made by scarifying the entire flank of the cow which allowed the production of a large quantity of vaccine. (Remember, this was during the 19th Century - more recently, vaccina was produced in cell culture). Even this century in India, cows and oxen treated in this way were led from door to door in order to deliver the vaccine 'fresh' to the inhabitants.
Jenner's original vaccine was certainly cowpox. It is not clear what happened between 1796 and the present day, but vaccinia's closest relative appears to be camelpox!