I think you are thinking about the smallpox vaccine. That’s the one that put a small circular scar on the arm.
Nope. The smallpox, diptheria, pertussis, were a separate vaccination. The polio vaccinations we had were in the 50's. I remember them vividly because all four of us kids had them. It was developed by Jonas Salk, and contained live virus, and it was given in, I believe, three different injections...the last one being the booster. It was injected intramuscularly, and within a few hours, the symptoms of aching, along with pain and discomfort when moving the arm, would begin. It would recede gradually.