You have to understand what distortion is, and what it does.
Distortion is clipping. Clipping turns a sine wave coming from your guitar into a square wave. In essence it “clips off” the top and bottom of the waveform.. The more heavy the distortion is, the more fuzz-like it gets. This is exactly what a fuzz pedal does - it’s a square wave generator.
When you clip off the top of the waveform, a few predictable things happen. First, the relationship between the bottom end and the top end of the frequency curve is altered. Things get more bassy because less high end gets through.
Second, the signal becomes more compressed. The more compression, the less dynamic range, and the less opportunity for the pickups to distinguish themselves in terms of tone or dynamic range. On the good side, I suppose, the more compressed the signal becomes, the more sustain it has added.
Anyway, when you compress a signal enough, and chop of the high frequencies enough, sure, most guitars sound very much alike. If all you play is very high gain stuff, the sonic differences between guitars will be obscured. Clean things up, and you hear the differences.