They are exactly the same, you can access the LCD in either 4 or 8 bit mode, 8 bit is slightly faster, but 4 bit saves you I/O pins.
HD44780 is an Hitachi number, and is the industry standard for text LCD modules.
For suitable PIC code check my PIC tutorials which give reliable proven code using 4 bit mode and either software or hardware timing. There seems very little reason to use 8 bit mode, except it makes the code slightly simpler.