What's the difference between "Initialize" and "Erase"?
Looking up the definitions, we find:


  Initialize:  On Apple Macintosh computers, initializing a disk means formatting it.


As erase is more a more generic term; from Merriam-Webster we get:


  Erase: 
  to remove (recorded matter) from a magnetic medium; also :  to remove
  recorded matter from erase a videotape; to delete from a computer
  storage device erase a file


When you initialize a device, you make it usable by the operating system.   When you erase a device/file, you remove the contents.  Initializing a device previously used with an incompatible format will inherently, erase the device.

To put it another way, you can erase without initializing, but you cannot initialize without erasing.  

diskutil's eraseDisk command requires you to specify the format so in effect you are always initializing the disk.

However, there is also the reformat command that, that allows you to erase an existing volume with same name and type.