Immunity: Protection from an infectious disease. If you are immune to a disease, you can be exposed to it without becoming infected.
That is a dumbed down wording of immunity. Protection does not mean, does not get, in actuality you must be infected first for your immune system to respond to the threat and deal with it.
If it was to say provides "complete" protection then you might consider that as the immunity you are searching for. Terms like you "can" be exposed and not get infected is a way of saying in most cases yes you wont notice you were exposed to a virus. Goverment agencies use wording like that to ensure people don't pick at the edges. Same way your antibacterial wipes say they protect vs 99.9% of bacteria. You will always get sick from the .1% if you challenge it in court.
Vaccine: A product that stimulates a person’s immune system to produce immunity to a specific disease, protecting the person from that disease.
If the vaccine removes 90% of severe symptoms vs a non vaccinated I would say it offers protection from that disease, just not "complete" protection.