I have used graphic and alphanumeric LCDs. I have come across LCD Display Drivers & LCD Display Controllers ICs. When are they needed and what do they do?
Display controllers receive high-level instructions from upstream ("draw the text 'ABC123' at the current position"), process/store them, and generates low-level instructions ("turn on pixels/segments X, Y, and Z").
Display drivers receive low-level instructions and turn them into waveforms for controlling commons and segments ("enable common 3, disable others, and turn on pixels 3, 7, and 12").