There are basically three types: inorganic zinc-rich primers, zinc-rich epoxies, and cheaper 1-component zinc-rich paints meant for repair and touch-up of hot dip galvanized surfaces.
Inorganic zinc-rich primers require a good surface preparation (at least a commercial blast and preferably a near-white blast) and they also require moisture to cure. We have noticed poor adhesion when these coatings are applied in the dead of winter where humidity levels are too low, but otherwise adhesion is excellent We have had no issues top-coating these materials.
Zinc rich epoxies have better, more reliable surface adhesion especially if surface preparation cannot be assured to be excellent. However, they provide poorer galvanic protection when compared against inorganic zinc which has been properly top-coated with an epoxy- but again only if the inorganic zinc is properly applied. We have trouble using zinc-rich epoxies here because we have several employees who are sensitive to either the vapour emissions themselves or to their odour- every formulation seems to contain butanol for some reason and it has a very pungent odour.
The 1-component zinc-rich primers and so-called "cold galvanizing" spray paints are better than nothing, but as coatings left for direct exposure to the elements, they're nothing to write home about. They need to be top-coated with something else to provide durable protection, but for aesthetic repairs to the cut ends of hot-dip galvanized items they do seem to do a pretty good job.