It is part of our job to figure out how much current a particular wire is likely to encounter, and then to select a wire that can handle that much current. A wire?s temperature rating (60C, 75C, and 90C are the common values) is based on the ability of its insulation system to tolerate that temperature, without melting or otherwise letting current leak to ground. A wire?s ampacity is the highest current that you can pass through it, under the specific conditions of its installation, without exceeding its temperature limit. That is the relationship between those two concepts.
The question then becomes, how do we determine the ampacity of a given wire, under the conditions in which we intend to install that wire? Table 310.16 has a column that applies to wires with insulation systems capable of handling a temperature rise of 90C. Given that we are assumed to start with an ambient temperature of 30C, that means the temperature of the wire could get as high as 120C, without damaging the insulation. If we keep the current below the value shown in the 90C column, then the heat generated by that current will not raise the temperature more than the 90C that the insulation is rated to handle.
But the wire?s insulation is not the only component at risk from excessive temperatures. We also have to consider the components to which the wires are connected. If we attach a 90C rated wire to a terminal block that has a 75C rating, then we are no longer allowed to use the ampacity values shown in the 90C column. That is because if we ran the 90C rated current through the wire, and through the termination point, the heat generated would not be enough to damage the wire?s insulation, but it might be enough to damage the termination. So we limit the ampacity of the wire to the value shown in the 75C column. That amount of current will be low enough such that the heat it generates will not damage the termination.