What is the difference between sleep, hibernation, and other power saving states?

Modern computer systems define a number of operating modes that determine what level of power they consume, these states are defined in the ACPI specification as follows:

• S0 - Working state.
• G1 - Sleep State.
• G2 - Soft off.
• G3 - Mechanical off.

Each of the states from S0 to G3 consumes less and less power with G3 representing a computer that is physically disconnected from power.

G1 defines a number of sub-states as follows:

• S0ix - Modern Standy, or Low Power S0 Idle. 
• S1 - The system is in an idle state, CPU and RAM remain powered and any device that does not state that it requires power may be powered down.
• S2 - CPU is powered off.
• S3 - This state is commonly called Standby, Sleep, or Suspend to RAM, and is the default sleep state for most newer computers.
• S4 - Hibernation or Suspend to Disk, in this state the computer's memory contents are saved to a hard disk and the system is powered down. At the restart, the computer restores the previous state of the computer from the disk.

The sleep states above again take less and less power as they progress from S1 to S4, eventually reaching a point at S4 that consumes the same power as the computer when in the G2 state (Soft Off). As the system progresses through these states the amount of time taken to return to the working state increases as well.