I thought I'd add a few more comments for those that are not familiar with compressors. There are 3 main features:
single stage versus two stage
oilless versus oil lubricated
tankless versus storage tank
In a single stage compressor, the air passes through the cylinder only once. A single stage compressor may have 1, 2, or more cylinders. The number of cylinders affects the volume of air produced (we'll talk about that later). In a two stage compressor, the air is compressed once in the first cylinder, then the compressed air is passed into a second cylinder where it is compressed again. This results in higher pressure. Two stage compressors always have pairs of cylinders, usually one or two pairs.
An oilless compressor has the cylinder and cylinder wall coated with Teflon. In an oil lubricated compressor, the cylinder has rings (that same as an automobile engine) and oil is introduced to the base of the cylinder to reduce friction. An oil lubricated compressor has a longer life expectancy than an oilless compressor. They also run quieter, usually quite a bit quieter. However, very small amounts of oil escape into the compressed air. Not usually a problem in commercial applications, where most tools require oil lubrication. But for painting applications, the air must be filtered.
The addition of a tank to the compressor serves two functions: first and foremost, it extends the life of the compressor by lowering the duty cycle. It does not increase either the volume or pressure delivered by the compressor. Secondly, it smoothes the delivery of the air. It a tankless compressor, the air is delivered in small (very rapid) puffs. Normally this is not a problem, but some artists fine it affects detail work.
When we say "compressor", we are typically referring to the complete unit: motor, compressor, and tank (if included). A compressor can consist of any combination of the above features, e.g. a two stage, oil lubricated compressor with a 60 gallon tank or a tankless, oilless, single stage compressor.
Compressors have two "ratings", the maximum pressure delivered, expressed in p.s.i (pounds per square inch) and the maximum volume available, expressed in s.c.f.m. or c.f.m. (standard cubic feet per minute). A compressor will typically list two ratings, such as 3.5 cfm @ 90 psi and 5.0 cfm @ 40 psi. The reason for these two ratings is that most commercial and shop tools run at either 40 or 90 p.s.i. Airbrushes rarely need over 50 p.s.i. (remember, the type of paint, it's dilution, and the effect desired determine the pressure) and consume between 0.25 and 0.5 s.c.f.m. If it helps, think of the p.s.i. rating as similar to voltage and the c.f.m. as similar to current.
Hope this helps.