yes, both contains GRAM...
But: ILI9341 (and others) are display controller, where you can directly access the pixel data within the GRAM und thus transfer the framebuffer content that is created by the MCU.
In case of FT813 - this is some kind of "intelligent" display controller, containing a audio engine, a touch controller and a graphics engine. The graphics composition is done directly on the chip, using simple commands to load a glyph or to draw a line. And this API does not fulfill the requirments to update framebuffer regions.
For more details, please have a look to the FT813 data sheet and programmers guide.
Best regards,
Manfred.