>what part of a car's innards a sump ...

Good we are agreed.

I think the sump is the bottom of the engine. I think that the instruction that I was given years ago was, "To change oil, position bucket, pull out sump plug, stand clear, replace sump plug and refill, the order of events, I recall was significant". Nowadays it is "Take car to garage, request oil change as part of expensive service, hand over dosh".