So the compressor will draw 13A at no load (imagine having it turned on, and flowing but not connected to a tyre). Once you start inflating a tyre, it will put additional load on the compressor and it will need to draw more current.

As for the Ah reating of the battery, mostly it's rated at 20 hrs, so a 50Ah battery will be able to supple 50/20= 2.5A per hour for 20hrs until discharge.

Someone might have a better explanation, but that's the short story.
There's also a number of tools out there to help calculate the Ah requirements of a battery bank given a known current draw. When you start adding solar input and everything else back in, then things change again... It's a bit of a black art