My thinking has been:
P&G - pulsing and gliding, engine can be on or off
EOnC - Engine on coasting, term generally used when coasting up to a red light or a reduced speed limit etc with engine on.
EOC - Engine off coasting, same EOnC with the engine off.
As I see it, P&G is a combination of techniques, whether you use EOC or EOnC as part of it doesn't really change the idea behind it, engine off just gives better results.
I've never assumed engine on or off, as many people aren't comfortable driving with the engine off (myself included) or can't because they have an automatic transmission.
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