Voltage Drop and current carrying capability are related, but two different animals when it comes to sizing conductors. You have to look at both, especially long runs. Typically, anything under 200 ft usually isn't an issue, but as they approach this distance, and certainly longer distances a quick check is prudent.
The long and short of it, the amount of copper required to carry the current is based on surface area of the copper (kcmil). As the current flows, heat is generated due to the resistance in the copper. The maximum continuous currrent the cable can take without exceeding the temperature limits is what is supplied in Table 310.16, and others. The heat is also why conductor amapcity ratings must be decreased when multiple conductors are in the same conduit. (heat from one set is superimposed on the other)
The voltage drop is based on the resistance of the copper and the maximum amount of current that will be flowing through it. I x R_cable = VD of cable.
This voltage drop is subtracted from the starting voltage to get final (load) voltage.
So, although the cable may meet the voltage drop requirements, it may not have enough surface area to adequatley carry the current.
Rule of thumb: Size conductors based on current, check voltage drop, and UPSIZE if required. NEVER downsize.