I would say this distinction is often just a semantics argument designed to calm the public. In common usage, it means you won't have a significant infection that becomes contagious. The vast majority of vaccines are successful at preventing that type of infection for a long time. Though there are exceptions.

By defining "infection" so broadly it loses all meaning, some officials are trying lump to the covid vaccines (which are no longer very good at preventing contagious infections) with vaccines that prevent contagious infection for decades. Obviously, the effectiveness of vaccines is nuanced and their effectiveness at preventing contagious spread is a spectrum--not a binary.

Public health officials should just be straight with us. The vaccines aren't as good as some of the vaccines we all get--like measles--but they do provide a great deal of protection. It's still basically a miracle that we got the protection we did in about a year after the virus appeared. It's a huge success.

I thought a big part of the tragedy of the measles vaccine rates dropping is precisely that we’re losing herd immunity.

At 95%+ immunised outbreaks ought not occur because herd immunity, even for the remaining unvaccinated, whereas at the lower levels, outbreaks will likely happen.

Is that not right?

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.