Larger LCD screens all use VGA or VGA-like interfaces - there is no screen buffer so you have to have a VGA-like driver to interface to them.
Small LCD screens (upto about 320x240) can have framebuffer chips like the ILI9325. These often have a simple-to-use serial or SPI interface which is easy to drive from a microcontroller (no requirement for constant refresh).
The reason for the difference between large and small screens is simple - the smaller screens have a single silicon chip controller which controls source and gate lines to the TFT LCD pixels - thus it can drive pixel data from a frame buffer to the right screen pixel.
Larger screens have separate (often multiple) chips for source lines and for gate lines. No one piece of silicon knows both the row and column information so there's nowhere to put a framebuffer (other than in an external VGA-generator chip).
With VGA style interfaces the source driver(s) handles Hsync and does serial->parallel conversion for one row at a time. The gate driver(s) handle Vsync and selecting the current row.