Difference between sleep, hibernate, etc
Sleep refers to when the machine pauses processes and such but with the RAM still powered.


  What happens when the Mac goes to sleep (not just into idle mode or display sleep)?
  
  On all Macs:
  
  
  The microprocessor goes into a low-power mode
  Video output is turned off, and a connected display may turn off or enter its own idle state
  Apple-supplied hard disks spin down; third-party hard disks may spin down
  
  
  On portable Macs:
  
  
  The Ethernet port turns off, if applicable (see note below)
  Expansion card slots turn off
  The built-in modem, if present, turns off (see note below)
  An AirPort card, if present, turns off (see note below)
  The USB ports only responds to the power key on an external keyboard (see below)
  The optical media drive, if present, spins down
  Audio input and output turns off
  Keyboard illumination, if a feature of your portable computer, turns off
  
  
  A computer uses considerably less power when in sleep mode than when awake. The computer will continue to power RAM in sleep mode, so that whatever was in RAM when the computer went to sleep will still be there when the computer wakes. This also means that computers with more RAM use slightly more power in sleep mode.


https://support.apple.com/kb/HT201714

Hibernation is called Safe Sleep in macOS. This is where the contents of the RAM is saved to disk.


  OS X includes a deep sleep mode known as safe sleep. Your Mac may enter safe sleep if your battery begins to run low, or your computer is left idle for a long time. Safe sleep copies the contents of memory to your startup drive, and powers down the computer. This helps you when your battery is depleted on Mac notebooks. All you have to do is connect your notebook to AC power again to pick up where you left off, without losing your work.


https://support.apple.com/kb/HT202824


  Safe Sleep ensures that data stored in the main memory of your Mac isn't lost when the computer shuts down due to its battery being drained completely. 
  
  Before your Mac enters sleep, Safe Sleep automatically saves the contents of its main memory — like desktop settings, open applications, and other work in progress — to the hard drive.


https://support.apple.com/kb/HT201635

Idle sleep is not a sleep mode, but rather a description of how Sleep can be activated: through the machine being idle for a set period.


  When you leave your computer idle, OS X automatically turns off or powers down features that you aren't using. When the computer needs to perform a task, related components are powered back up.


https://support.apple.com/kb/HT202824

Standby mode is similar to Safe Sleep but used when your machine has an SSD.


  For Mac computers that are started from an solid-state drive, OS X includes a deep sleep mode known as Standby Mode. Mac computers manufactured in 2013 or later enter standby after one to three hours of regular sleep. A computer with a fully charged battery can remain in standby for up to thirty days without being plugged in to an AC power source.


https://support.apple.com/kb/HT202824


  Mac notebook and desktop computers have a power standby feature that conserves energy. During standby, the state of your session is saved to flash storage (SSD). Then, the power turns off to some hardware systems such as RAM and USB buses.


https://support.apple.com/kb/HT202124

pmset's autopoweroff sets the time it takes from Sleep starting until Safe Sleep is initiated.


  autopoweroff - Where supported, enabled per default as an implementation of Lot 6 to the European Energy-related Products Directive. After sleeping for &lt;autopoweroffdelay> minutes, the system will write a hibernation image and go into a lower power chipset sleep. Wakeups from this state will take longer than wakeups from regular sleep. The system will not auto power off if any external devices are connected, if the system is on battery power, or if the system is bound to a network and wake for network access is enabled.


https://developer.apple.com/legacy/library/documentation/Darwin/Reference/ManPages/man1/pmset.1.html