Enamel paint is defined more by its qualities than by its content. In the broadest sense, enamel paint means any solvent-based paint that dries to a hard, vitreous (glass-like) shell. Solvent-based paints are also called oil-based paints, in contrast with water-based paints.
Enamel paint springboards off of its root words “smelt” or “melt,” since true enamel is a glass coating that is melted or kiln-baked at extremely high temperatures onto metal or ceramics. Note, however, that enamel paint bears no similarities with the enamel of molten glass, as there is no glass content in this kind of paint. Even traditional baked enamel finishes, long used for vehicles, have nothing to do with glass. The baking is simply a fast route to eliminating solvents and VOCs.
In reality, air-dry enamel paints are far softer than true enamels formed in a kiln. Paint manufacturers have further widened the definition by sometimes attaching the word enamel to water-based paints, thus losing the one ingredient that usually ties together all enamel paints: solvents.