My understanding was that a vaccine would immunize the recipient, preventing infection and reducing the number of vectors for contagious diseases to spread.
Flu shots were an amalgam of likely strains that were meant to reduce the severity of flu infections and thus reduce the number of hospital stays and deaths. It would not immunize you, though it would probably reduce transmission to some extent.
The COVID shots sound a lot more like a flu shot than a vaccine. But we've updated the definition of 'vaccine' to include shots like the flu shot, which do not immunize but are meant to blunt the severity of flu season. I wish we'd found a different term for the COVID shots, because the word 'vaccine' no longer means what it used to mean.