Battery choice/source help?

Mostly correct.
A batteries capacity , in this case 110 mah , is rated at a particular discharge rate, and its usually 0.1C , but LIPOs are better, hence in this case 0.2C.
This means that if you discharge the battery at 0.2C, 22 ma it will take 5 hours to discharge the battery.
If however , you discharge the battery at 2C, 220 ma, the battery will be discharged in less than 30 minutes.
The differance is made up because of the fact that the battery heats up when discharged at a high rate,
so the heat energy is lost , and not available as electrical output.