To me, a "pony bottle" is a small cylinder of gas that you take with you in addition to your main gas supply, with it's own separate regulator and (maybe) an SPG. It is used ONLY as a emergency gas source, for either you or another diver. If anyone has to use the pony, the dive is OVER. It is not factored into your gas planning calculations.
...or maybe a bottle full of ponies? Really small ponies or really large bottle
To me, a "bail out" bottle is something rebreather divers carry in case their rebreather quits working and they have to bail out to open circuit to get home.
A "stage" bottle is a bottle carried specifically in order to extend one's dive time, and is factored into the gas management plan.
A "deco" bottle is filled with hyperoxic gas and is used to shorten one's deco obligation