Physicist's point (I think) is that not all temporally well-ordered events are causally connected, though surely all causally connected events will be temporally well-ordered.
This implies that the set of causally connected events is a subset of the set of all temporally well-ordered events.
I hope that's clear.... because there'll be a quiz next period!
Well, yes. But ... when we observe an event from a distant frame of reference (a supernova will do as an example) it's entirely clear that such event is the result of a causal sequence which is entirely outside of our local sequence of events. This doesn't alter my original statement that the causal sequence of events, moving as it does in one direction, from cause to consequence, underlies our concept of the "flow of time". It's entirely true that we are always getting information from unconnected sequences (that is, from distant frames of reference). Which means that not all events are causally connected (unless you go back to the Big Bang, in which case they are). I still maintain that the cause & effect sequence literally is the direction of and the ultimate nature of time. No causal sequences, no time.