The main difference is that the F30 has some manual controls (aperture priority and shutter priority) that are missing from the F20.

People who are into photography prefer the manual controls.

Both cameras have "modes" which lets the user get better results under difficult situations, without resorting to manual controls.

Here is a look at the press release of the F20:

The F20 can be found for under $200 and would make an excellent camera for your mom. There is little point in looking further if the price is right for you.