NEC doesn't apply to appliances, only infrastructure. An appliance designed for 50A can draw 50A, continuous or not.
This seems like a debate for another time. The NEC may not have jurisdiction over appliances depending on where you are, but it certainly has guidelines for construction and such of some specific appliances, like EVSEs, that it definitely makes sense to adhere to. Keeping in mind that the NEC is put out by the NFPA (National Fire Protection Association) I tend not to argue too much with them.
With regard to the continuous load provisions, the technicality behind it is that supply equipment is not actually "derated", but rather circuit conductors and OCPD's must be sized for 125% of the offered continuous load. This means you start with the load (40A or 80A) and then size conductors and OCPD's at 50A/100A, not the other way around. It may seem like the same thing, but it makes a difference when it comes to calculations like applying derating factors and such.
You are correct. I'll be more careful with interchanging those terms in the future.
Never-the-less, it would be my hope that Tesla would have designed the adapter with the 1.25x rule in mind.