Have you ever thought about why amp head has "overdrive" channel and pedal is named "distortion"? They are slightly different.
1) Amp head. Why do you hear this crunchy sound? (on tube amps, for example). Because you play notes with different volumes. And you just "push" a part of your signal over the "distortion point", which could be played by amp. So, your signal becomes cut (sine wave becomes edgy).
2) Pedals. In the first example "distortion point" was constant. But here we can just tweak "Gain" know and bake this "point" easier to reach....
