Both lacquers and enamels can be pigmented or colored. Lacquers are thermoplastic or can be completely dissolved in the solvent they were made with. Lacquers dry by solvent evaporation.
In contrast, enamels cannot be completely redissolved in their original solvent. The solvent may lift and or remove the enamels, but there will be flakes and undissolved particles left behind. Enamels dry by solvent evaporation and then cure by oxidation (a process where oxygen reacts with the polymer vehicle to form a new oxidized polymer) or crosslink with another polymer added to the enamel.
Think of a scrambled egg. If you let the uncooked scrambled egg dry completely by evaporation, you can make scrambled egg again by adding water. The dried egg film is equivalent to a lacquer.
If you fry the scrambled egg solution, the egg will not redissolve in water. The proteins in the egg have crosslinked to form a new polymer. This is equivalent to an enamel.