Epoxy paint differs from other paint because it contains resins. Resin comes from plants, such as pine trees, and dries to a transparent, glossy finish. Enamel paint is made from solvents and binders that dry to a shiny finish, but it does not contain resin.
Enamel paint contains methane, which is a solvent. Methane is a hydrocarbon that is colorless and odorless. Methane is actually one of the Earth's greenhouse gases -- naturally occurring in our environment. It gives the enamel paint its smoothness.
The cost of epoxy is significant, so use it for "industrial use" jobs such as painting a warehouse floor or carport floor area. Driving on the painted epoxy surface or rolling heavy equipment will not dent or chip it. Enamel paint, however, although visually appealing and shiny, can easily stick to tire treads and come off.
You can use both types of paint in certain situations. For example, if you build a plywood boat, you can fill seams with an epoxy mixture and paint the rest of the plywood with enamel.
You can brush on enamel paint or apply it from a spray can. Epoxy, which has additives that give a "non-skid" texture, is difficult for a DIY application. Rolling it on a garage floor, for example, is a job for someone trained to do this who owns the correct application tools. Applying epoxy for a smooth finish requires specific drying times in between coats as well.
Enamel is used to provide a shiny topcoat, so it works well on an electric range or refrigerator made of metal. Metal surfaces that will get intense wear and tear, such as metal parts of bridges, will require epoxy applied as a powder coat and then baked on. You can use epoxy on projects that join metals, wood or plastic because it has adhesive properties. The chemical components of epoxy contain a hardener that adds to the toughness and resiliency the resin provides.