From a build quality and light control standpoint, PAR type lamps are generally considered superior. The explicit parabolic nature of the reflector means light is more precisely reflected directly out of the bulb cavity, with less dispersion, than an R or BR type lens. PAR type lamps, thanks to the design of the lens in front of the actual light emitting element (which is usually a given with home lighting…PAR in general can referr to a very wide variety of lighting which may or may not have a front lens, including high powered stage lighting). The lens is often fresnel in nature, are often additionally capable of focusing the more accurately reflected light into a brighter, narrower spot. The fact that they have a more precisely crafted lens means they are capable of being designed to emit beams of varying angular degrees wide (anywhere from 12° to 70°), with high intensity narrow beams or more diffuse wider beams, makes them highly flexible.
PAR type lamps are also frequently designed in such a way that makes them viable for outdoor use. Not all PAR type lamps are properly sealed for use in humid climates or areas where rain or other water could intrude upon the bulb, but many PAR type lamps are. This is a key difference between PAR and R or BR type lamps.
In terms of nomenclature, PAR lamps are usually designated with a number. The number of a PAR lamp, such as PAR38, gives the diameter of the lamp in inches. In the case of a PAR38, the diameter would be 4.75″ (4 3/4″), or “thirty eight eighths of an inch.” Common PAR lamp sizes for home are PAR20, PAR30, PAR38, with the latter being most common.