Yes, the reason is that NM-B is surrounded by a plastic/rubber kind of sheath, which is kind of insulating and traps the heat in, so needs to have a more protective temperature rating. MC cable is surrounded by a metal jacket, and with metal being such a good heat conductor, it can more easily let that heat out to the outside environment.
Hmmm. I have seen many forms of ampacity tables before. That is the first one that I have seen which says the ratings are for "continuous", and I did not think that is how the ampacity ratings are used. So I just did some digging. It was a little hard to find, but I did finally find an example showing how to choose wire type and size, given the load:
This gives an example where the load is 53A continuous and then calculates from there for oversizing and selection of breaker and conductor on page 2 of this PDF:
"Select the conductor to comply with Sections 110-14(c) and 210-19(a). Section 210-19(a) also requires the branch-circuit conductor to be sized no less than 125% of the continuous load, 53 amperes x 125% = 66 amperes. We must select the conductor according to the 75' C terminals temperature rating of the equipment terminals. No. 6 THHN has a rating of 65 amperes at 75' C and can not be used. Therefore we must select a No. 4 which has a rating of 85 amperes at 75' C."
That's how I thought it was applied. You do your calculations based on whether the load is intermittent or continuous, to find the appropriate amp rating number of the circuit first. And then the numbers in the ampacity tables are the number to match to that amp rating number of the circuit.
That's not rounding it down then. You said you are using the wall connector at its maximum allowed capability, which is the 48A continuous load setting. Using their calculation example from that NEC explanation document, you take the 48A continuous load times 125% to find the circuit rating needed, which is 60A. Then, you need to select conductors that have a number listed in the ampacity table to meet 60A. 6 gauge NM-B is not high enough.