Do different video cards have different speeds? Which is faster of the two: Geforce2 128MB(128bit) & Geforce4 64MB(64bit)? If anyone can explain how a video card works, I would be most greatful.
Thank you in advance.

On a basic level today's video cards basically control the calculations to put out all the fancy video for today's latest games etc. Much of this was formally done by the computer's CPU. They use a type of high quality RAM to do this. Of the two cards you listed the GeForce2 has twice as much of this RAM as the GeForce4. This of course is only one of the differences between the two cards.
Today's video cards also use a special AGP slot on the motherboard. This increases the bandwidth or the amount of data that can be pushed through. In general AGP4x is 32bit and 8x 64bit. So your example is using bytes (or megabytes)of RAM. The bit issue is something else.