"Video card" was the more general word. "VGA" is one of the IBM video cards for PCs that later became a de facto standard, as its behavior was cloned by other companies. It's sometimes used descriptively to talk about the 640x480 resolution, or the DE-15 connector that remained a standard connection for analog video output on personal computers for a long time.

There were a series of graphics adapters that started with the IBM PC:

MDA = Monochrome Display Adapter (text only) https://en.wikipedia.org/wiki/IBM_Monochrome_Display_Adapter

CGA = Color Graphics Adapter https://en.wikipedia.org/wiki/Color_Graphics_Adapter

EGA = Enhanced Graphics Adapter https://en.wikipedia.org/wiki/Enhanced_Graphics_Adapter

VGA = Video Graphics Array https://en.wikipedia.org/wiki/Video_Graphics_Array

With some others like the Hercules which was MDA upward-compatible and did graphics as well as text.

They didn't really do any graphics "processing"; just displaying memory-mapped pixels in various formats.

They were memory-mapped, and the MDA used a different memory block than the CGA/EGA/VGA, so you could have two separate monitors simultaneously, doing things lke running something like Turbo Debugger on the MDA text display.