You're talking about a simplified "pop" understanding of what a vaccine is and does. Even in elementary school I wasn't told that a vaccine prevents disease; I was told that it provokes an immune response that provides resistance to a disease.

The fact that people confuse the two is a legitimate public education problem. But it doesn't change what they actually are, or how medical professionals use the word.

> But it's a secondary effect, otherwise we would call more things "vaccines", as we know that for example "exercise helps with immune response".

It is the effect. I think everybody understands the difference between taking care of yourself and receiving a medical preparation that stimulates your immune system against a specific disease.