A graphic EQ allows you to cut and/or boost a specific range of frequencies. This range is determined by the filter design of the individual bands, set by the factory. Some models have bands that are 1/3 of an octave wide, others can have bands that are wider-1/2, 2/3, 1.0,1-1/2,etc.
These bands are set on pre-determined centerpoints ("fixed frequencies"). All you can do is adjust their gain.They are referred to as "graphic" because the vertical sliders give a "graphic" representation of the audio spectrum "curve" that has been adjusted.
A parametric EQ permits the operator to not only set the cut/boost of a given band, but also the center frequency and the BANDWIDTH of that band. Typically, a band may be as narrow as, say, 1/6-octave, to as wide as 3.0-octave. The center frequency of the band is tuneable over a wide range, as well. So, instead of a single control per band, there are 3. A "semi-parametric" EQ has cut/boost, a frequency "sweep" control, but no bandwidth control.
Parametrics excel at "honing in" on a problem frequency band and minimizing it. This can be a loud "hot spot" on a bass guitar, or a resonant node prone to feedback in a live situation. You can also set up a much wider band than the typical graphic EQ can do, allowing you to use it as a gentle "tone control".
The graphic EQ is typically used to set up the overall response of a given sound system. It is limited by its' fixed frequencies and bandwidths, but is easier to operate. Because of the simpler filter design of the individual bands, it is less expensive to manufacture. Both designs have their place.

Well said, Moon!
8-)

Thanks
Now I get it. As a ham radio operator, I know that in electronic terms it is the Q factor of the filter that you are adjusting as one of the paramaters that determines the slope of the filter curve.

That is correct.