How does primer differ from non-primer paint?

This depends somewhat on the primer.  With some, their purpose is just to act as an intermediary between the substrate and the paint. In other cases, they are formulated to also act as corrosion protection and chemically bond well with the substrate, especially primers made for going over metals.  Red oxide primer, for instance, is a good corrosion protection as well as a primer.  Zinc Chromate primer, now very hard to prime, is another of that type, especially good on aluminum.  Some primers have more filler/pigment to cover up tiny scratches and imperfections, such as auto body primer.

Primers are usually just stronger paints that bite onto the plastic, but in the end, they are just paints. Most are designed to spray or airbrush easily...not hand brush. Concerning Vallejo, their primers are acrylic-urethane and are a bit stronger than their basic model air/color paints.

Really, the whole idea of primers wasn't originally to help hold the paint down. In the early days of modeling (as with most non-artistic painting projects of today), the primer was simply a means to have a standard overall shade to paint on...thus requiring fewer coats to get the right color. This is why primers are typically a medium grey, not wild orange. For instance, house paint sticks to wood just fine, but it's hard to paint white over a dark wood. So, it's usually easier to paint a light grey primer first, then go back with the white paint.

With enamel-users, primers weren't a necessity. Some people still used them, but they weren't much different from the enamel paints they already had, and there was no fear of paint lifting off either way.

These days, with acrylics users, primers are essential to hold the paint down, and that's what we typically go to a primer for. Of course, you can just as easily spray any lacquer or enamel paint down as a primer.