R-Type lamps are found in sizes varying from about 2.5" in diameter to 6.5"+ diameter. They are for in door use only and are found in several styles of border lights (r-38 and R-40 primarily). They throw a nice punch of flood light out in a more concentrated pattern than an A type lamp and can come in wattages from 60 to about 500 watts.
PAR- Type lamps use a Parabolic Alumanized Reflectorsystem with a glass lens on the front that usually varies the field diameter. PARS are available from PAR-20 to PAR-64 and vary from around 50 watts to 2 kilowatts. PARS are a heavy duty version of the R type lamp and have an "axis" of light because of filament geometry, usually PAR type lamps have a beam that is twice as long as it is wide. The beam spreads are as follows (VNSP, NSP, MFL, and WFL). The base is either a mogul screw base or a mogul end prong base depending on what fixture the lamp is being used in.
MR- type lamps are typically low voltage (12v-82v) but 120v versions are available. They are used to accent things such as art work. They are also the primary type of lamp used in several different follow spots (Altman Comet). The reflector on an MR lamp is design to absorb UV and IR radiation and reflect visible light. The field angles are any where from about 8° to 50°. The sizes vary from anything as small as an MR-8 (1" diam) to a standard MR-16 (2" diam) or sometimes even larger, but, the MR-16 is still the more standard of the sizes available.
I know nothing about K-type lamps, so maybe ship can fill you in on that