Rich,
You started off just dandy with a correct description...
Then let these guys talk you into degenerating into slang terms, like "toggle" and "flip-flop".
Toggle is the name of a switch.
Flip-flop is a name long taken by a type of transistor gate, the "J-K Flip-Flop".
In most cases people use the first term they think of to describe a function, even though it is not the best name.
I applaud you for first using the can't-go-wrong "alternate". I would like to see the term "alternator" adopted here for the type of circuit that turns something on and off by repeatedly pressing one momentary-contact button (or by turning a PLC bit instruction on and off).
True, the terms "toggle" and "flip-flop" decribe what it does, but are not unique - they were better-applied to other things many years before PLCs were invented.
The term "alternator" has long been applied to a type of circuit that switches control of pumps or compressors from A to B. It seems appropriate to add this PLC-equivalent version to the definition.