If I remember my biology and music theory classes, there is no biological difference in how WELL people can sing. Their range is determined by the length of vocal chords and how strong their diaphragm is.

Musically, people are able to sing better with no training because they have some form perfect or relative pitch(not going down that road right now) which is just that they inherently know what to sing. The only real way to be able to sing well is to practice, you just have to stop caring about your voice and sing. It's been proven in studies that over time, people are able to match pitches better and that moves into singing better.

For example, I had a terrible voice, even though I had musical training as a percussionist. I just decided I was going to sing in the car and over time I noticed that I was able to pick up and match notes with the singer and that I could even match their tone and sound of their voice(you should hear me sing Hamilton sometime).

To address something else that was asked, your voice in your head actually is in the pitch you hear it is just more "full" to use a musical term. You hear the resonance of your voice within your skull, but it still has the same pitch, because that is only changed by the length of your vocal chords. You sound different because you have a different tone, which is the quality of sound.