For working with compressed air, you will want a compressor with a storage tank, and a regulator. A pressure switch to keep the storage at a set pressure is also desirable.
The compressor shown above is just that - a compressor used for inflating things like tires and sports balls. Turn it on when you need air, and turn it off when you’re done. It delivers high pressure, but at low volumes, and it can take a while to provide any significant quantity of compressed air at useable pressures. If you’re going to be using the air to power things, be it tools or air muscles, you’ll want the ability to source large quantities of it on demand, without having to wait for a compressor to deliver the pressure you need a small volume (the displacement of the pump piston) at a time. For this, you will want a storage tank of some sort.
A regulator allows you to deliver a set pressure, without worrying about blowing your seals, lines, actuators, etc. This is generally a good thing, because things exploding under high pressures is a situation that is generally best avoided.
Finally, a pressure switch handles the supervisory task of keeping your storage tank at a useable level, turning the pump on when the pressure falls close to your minimum working pressure, and turning it off again when you have enough in the tank.
Fortunately, many commercially available compressors come with all three of these components already assembled into one nice unit, with a minimal risk of sudden unplanned decompression. You can also bodge together your own set, but the chance of inadvertent self-disassembly is much higher, and the savings aren’t really that great.
For a while, I ran my airbrushes off of a compressor set that I had hacked together using a spare tire, a 12-volt tire pump (like the one pictured above), and a recycled pressure switch salvaged from a water tank of some sort. The assembly was hooked up with an assortment of barb fittings, air hose, and clamps. It worked, but I probably spent just as much time on repairs and tracking down leaks as I did on using it for painting. After a rather sudden and dramatic failure under pressure, I finally got smart and bought myself a real compressor with the pump, regulator, tank, and switch all in one unit. It was well worth it, and getting rid of my “compressor of death” was probably one of the wisest purchasing decisions I made.