The original definition of vaccines included that they prevented infection (in the case of viruses, infection is when the virus replicates in the body). The most recent definition is that they merely promote an immune response. The average person who took the shot probably believed they were getting the former definition and that it would prevent infection. They were told that “breakthrough” infections would be rare.
https://www.usatoday.com/story/news/factcheck/2021/11/30/fact-check-merriam-webster-changed-vaccine-definition-accuracy/6354415001/
According to an archived version of the dictionary's website, Merriam-Webster formerly said a "vaccine" was "a preparation of killed microorganisms, living attenuated organisms, or living fully virulent organisms that is administered to produce or artificially increase immunity to a particular disease."
The new definition of "vaccine", published in May, reads: "a preparation that is administered – as by injection – to stimulate the body's immune response against a specific infectious agent or disease."