I think one of the problems in this thread is the confusion of using
"phase" to refer to both true phases as in 3-phase versus the 180-deg
phase difference between the two hot legs of a single-phase AC circuit.

I don't know when it became prevelant or popular (if it actually is or
whether it's still fairly isolated) to refer to the two hots as two
"phases"

As I understand it, everything is pretty much the same whether you have true
240v (one 240v hot and a 0v neutral) or "2 phase" 240v (two 120v hots 180
degrees out of phase). Everything will work identically. (With the
understanding you would need a 120v "neutral" in the first instance to get
120v to H-N)

However 3 phase electricity is very different. Or so I have heard.

I think that is why 240v is not called "2 phase"; it can be thought of as 1
phase, but is completely different than 3 phase.