We are getting into some testing esoterica. The wire ratings date from some IEEE work, originally done back in the '30's. There is a rather convoluted method used to determine the temperature an insulatio may be exposed to, over extended periods, without 'significant' deterioration in the insulating ability of the insulation.
When a new wire comes out, it is generally compared to existing wires, and classed accordingly.
Take, for example, THHN. A pvc insulated wire with a nylon jacket. Sounds simple? Sure- ask DuPont. There are thousands of varieties of "nylon", and an infinite variety of "pvc." Yet, wires from different manufacturers, using varying compounds, all get clased as "THHN."
There are sundry tests used to class, or verify the classification, of a wire type.
We drift, here, however. What is important is to note that (for example) a 60 degree wire may be exposed to 60 degrees for a long time, before the insulation deteriorates. We use that figure ... adjusting for ambient temperature, bundling, etc., ... to adjust the table "ampacity" to our overcurrent protection.
Now... we've done all that. The wire ought to never exceed 60 degrees, as we have calculated. We next attach it to a breaker rated to withstand 75 degrees ... how can there be a problem?
Or, looking at the reverse situation: You have THHN - a common 90 degree wire - that your calculations show can reach 80 degrees. Are you OK? Not if the breaker termination is only good to 75 degrees! The wire might be fine, but the termination will fail.
The breaker rating does NOT influenc the wire type; it DOES influence HOW that wire is used. ANY insulation type can be used on ANY breaker ... IF the calculated temp of the wire will not exceed the rating of the termination.