“Vaccinia virus (VACV or VV) is a large, complex, enveloped virus belonging to the poxvirus family.[2]
“It has a linear, double-stranded DNA genome approximately 190 kbp in length, which encodes approximately 250 genes. The dimensions of the virion are roughly 360 × 270 × 250 nm, with a mass of approximately 5–10 fg.[3]
“The vaccinia virus is the source of the modern smallpox vaccine, which the World Health Organisation used to eradicate smallpox in a global vaccination campaign in 1958–1977. Although smallpox no longer exists in the wild, vaccinia virus is still studied widely by scientists as a tool for gene therapy and genetic engineering.”
https://en.wikipedia.org/wiki/Vaccinia
Vaccinia virus is why vaccines are called vaccines.
Vaccine became a generic term, like Kleenex for tissues etc...