A graphic EQ is designed to cut or boost level on equally spaced frequencies, such as 1/3-octave or octave spacing, with a preset bandwidth value. Parametric EQ, on the other hand, gives you fewer EQ bands, but with more control, letting you vary the center frequency of the boost or cut, as well as the bandwidth of the adjustment.
Graphic EQs are popular for live sound installations, in which you want to use EQ as an overall shaping tool for the sound, for stage monitor tuning, and other applications. However, if you want to make more “surgical” corrections, such as when recording, a parametric EQ gives you more control.
So, broadly stated, graphic EQs are great for shaping, while parametric EQs are useful for fine tuning.
But these aren’t hard and fast rules. You may find that you have a favorite graphic EQ that has preset frequencies at very musical divisions. Or you may find that the acoustics of a particular live venue or a monitor feedback problem benefit from a “surgical” notch at a trouble frequency, something a parametric EQ excels at. Don’t be afraid to experiment, and find what works for you!