The type of insulation used determines the maximum ampacity of a wire. In reality, this maximum must also be derated for safety (normal load should be 80% of rated ampacity), ambient temperature, armoured sheaths, raceways or adjacent power conductors.
The first site is more:
As you might guess, the rated ampacities are just a rule of thumb.
Long power runs, assume 15A for #10.
The Maximum Amps for Power Transmission uses the 700 circular mils per amp rule, which is very very conservative.
Short power runs, assume 55A.
The Maximum Amps for Chassis Wiring is also a conservative rating, but is meant for wiring in air, and not in a bundle.
They protect their butt by:
NOTE: For installations that need to conform to the National Electrical Code, you must use their guidelines. Contact your local electrician to find out what is legal!
If you figure a maximum of 3% voltage drop to a feeder, this means a specific maximum distance for #10.
At 120V, 3% means 3.6V. At 30A, this equates to a feeder resistance of \$0.12\Omega\$ or feeder length of 120ft or 60ft from panel. 30A with a load 60+ft from panel violates the 3% maximum voltage drop. Too much current for the insulation, which would go through irreversible deterioration and possible fire, death and destruction.
You could do the math and figure out the correct size of wire for the wire distance or using their rule of thumb and half the current. To get 30A, double the area or #7.