Amps is a measure of actual electron flow. The max current is a fudge based on the cross sectional area (gauge), reasonable heat dissipation, and the amount of voltage drop you are going to see at the end of the wire (the wire is not a perfect conductor - there is a conductance number that is calculated based on the material the wire is made of and the cross sectional area. You multiply this by the length of the wire to figure the equivalent resistance, which can then be used to calculate the voltage drop at the end of the wire when under full load.)
To run 20 amps ~ 25 feet, I would suggest 12 gauge wire... If you are going 50 feet or more, you should up it to 10 gauge.
The great thing about using 12v systems to power our stings is that we can tolerate about a 4 to 5 volt drop in the line voltage before things start shutting down. If you are using a 5 volt system, even a 2 volt drop is gonna cause problems.