Circuit amps vs device amps
Basically, a 20a circuit can provide UP TO 20 amp, and a device draws what it says it requires.

That's it.  You've answered your own question.
To add on an extra layer - that is true for any constant-voltage distribution system; AC, DC, whatever.  The way to analyze it is that in such a system, the output voltage of a theoretically perfect voltage source never changes no matter what the load is, and the output impedance of the source is zero ohms, or a very low number.  The output impedance is essentially a very small resistor in series with the output of the perfect power source.  The complete circuit is the voltage source, its output impedance, and the effective impedance of the load device (light bulb, vacuum cleaner, whatever), all in series to GND.
Thus, the source's output impedance and the load form a voltage divider; the midpoint of the divider is the effective output voltage of the source as seen by the load.  With Ohm's Law, you can see that the load impedance must be very low before the voltage it sees begins to sag.  This means that the current through the circuit is almost completely dependent on the impedance of the load, from a cell phone charger all the way up to an electric clothes dryer.
There are other types of systems, such as constant current and constant power, but those are not nearly as common, and more complex to analyze.