Roman Bystrianyk wrote:

What you're referring to is variolation, which is infecting
someone with a weakened smallpox. Vaccination (from the Latin)
for cow is inoculating with cowpox to prevent smallpox.

Jenner thought he was using cowpox. However, it's
a great mystery just what the Vaccinia virus is.
It could be a modified smallpox virus, a modified
cowpox virus, a smallpox-cowpox hybrid, or a virus
distinct from both smallpox and cowpox. Nobody knows
where it came from. There may be a natural host
harboring the Vaccinia virus, but none has yet been
discovered.