The needle (really needles) I, and lots of folks I know, got jabbed with looked like this: Mine, however, wasn't attached to a thing that looked like a TOS phaser, but a spinning top. It tended to leave a circular scar on people's shoulders.
I split the Dayton derailment into the thread made for it. On topic: I was told I got that vaccination as a child, but didn't have the scar. I do now because they vaccinated me in Army basic training.
That sounds like an urban legend. I got the smallpox vaccine (from the Army) back in ‘06 and don’t have a scar.
The vaccine has changed considerably over the years and there were batches used in the late 60s/early 70s that were ineffective, and how you're able to tell if you got one of them is that you don't have a scar. I know more than a few people my age who do have the scar. Some time after I was in the prime candidate stage for getting the vaccine, they reformulated it again, and those are said to be more effective.