No, sleep and hibernation are not the same thing. Hibernation (aka deepsleep) writes the entire contents of RAM onto the hard drive. In OS X (unlike Windows), hibernate doesn't actually result in a shutdown that conserves battery life while allowing you to pick up where you left off (another case of Apple knowing what is best for you). Instead, it works in conjunction with, and as a safety for, regular sleep. Basically, if you have hibernate enabled in OS X, it will (should) write the RAM contents to disk when you choose sleep/close the lid. At that point it is just sleeping. If the battery goes dead while it is sleeping (or if you pull the battery), then upon reboot OS X will (should) load the contents of the sleepimage file back into RAM so that it will pick up right where you left off (all apps etc. open) just as if you had been able to wake it from sleep normally.