A graphic equalizer boosts or cuts certain frequency ranges in volume. It has less control over the frequency range than a parametric equalizer (which, as the name indicates, allows you to set parameters on the boosts and cuts).
So it is kind of like changing the music to make certain parts of it sound louder or softer. This is not really analogous to changing the speaker, in the same way you might ask a pianist to play certain keys harder or softer but it will still sound like the same piano.
Since it is easier to hear louder things, and harder to hear softer things, just because you now notice something more does not mean that what you were hearing before was incorrect or that your equipment was lacking. (Like above, same piano, just some notes louder or quieter now.) Without doing a measurement of your speaker's frequency response in your room, you can't really say for sure that the boosts or cuts you have added are making things more correct or actually less correct, even if it sounds better to you.