Actually, its the exact same thing, apple calls it safe sleep, MS and the world calls it hibernation.
Heck in changing the sleep options you invoke within the terminal
pmset hibernatemode <value>
So even then apple is using the term hibernate 🙂
No, it's not the same:
Windows:
Sleep: set processor to sleep state, keep power to RAM contents (RAM refresh)
system power usage typically 0.1W-0.5W
Hibernate: store all memory contents to a file on the HDD and completely power off the system. Read RAM contents back from file upon "de"-hibernate.
system power usage: essentially 0. No data is lost when removing the battery.
OS X:
by default OS X does the above Sleep when closing the lid, but in parallel it also stores the RAM contents to HDD, so that if system power is lost (e.g. Sleep for a couple of days drains to battery to 0), then the system state can be resumed from the Hibernate file automatically.
Advantage: user doesn't need to think
Disadvantage: 10s delay when closing the lid whilst the HDD is still in use
Because I have an SSD, I use the SmartSleep control panel item (oops, I mean System Prefs), to tell it not to write a hibernate file - saving disk writes (and for mechanical HDD based systems, it means that you can move the machine instantly when you close the lid).