According to this BBC article, we hear ourselves bassy compared to how we sound to others.
What makes a recording of our voice sound so different... and awful? It’s because when you speak you hear your own voice in two different ways. Greg Foot explains all.
The first is through vibrating sound waves hitting your ear drum, the way other people hear your voice. The second way is through vibrations inside your skull set off by your vocal chords. Those vibrations travel up through your bony skull and again set the ear drum vibrating. However as they travel through the bone they spread out and lower in pitch, giving you a false sense of bass. Then when you hear a recording of your voice, it sounds distinctly higher.
How do we then sing in tune to a song? We must be doing a constant pitch correction while trying to reproduce a previously heard sound. How does this pitch correction actually work?
EDIT 2016.02.09: Added link to, and a quote from the BBC article which I've read before asking this question, and which reconfirmed a wrong assumption on which my question was based.