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.

Ok makes sense.

But is that different then to vaccines against bacterial diseases? If some bacteria enter my body, surely they don’t magically disappear either, maybe split a few times but eventually die off.

Herd immunity is a function of transmission not individual infection. Faster and stronger immune responses reduce the number of viruses produced inside someone over an infection. That directly means they are less likely to infect other people.

Herd immunity is effectively a function of how infections something is. 1 case leading to 2 cases on average means you need to cut transmission in 50%. 1 case leading to 10 cases and you need to block 90% of new cases.

Critically this means vaccinated people can still be infectious as long as they infect less than 1 person on average you can reach herd immunity.