That is right. It is just immunity as a term in the medical community vs average joe use of the word. Medical community immunity means your immune system fights off the invaders before anything medically interesting happens, not that you have a magical force field that prevents entry. Not sure why people are trying to twist that into some sort of insidious plot.

If you have the measles vaccine and you get exposed to measles, measles will be in your body for a short time in low quantities, but your immune system will quickly destroy it. That means you are unlikely to pass it on or develop symptoms.