In other words what's the difference between the voice that is picked by a microphone and what the speaker himself hears when he speaks?
The voice you hear when you speak is a mix of the sound that comes out of your mouth and the bones of your crane vibrating. This probably has a very different filter from one person to the other.
I guess that most people hear some emphasis on the lower end and lack some airy details.
Usually in movies, they use a short reverb and a boost somewhere between 160 and 450 depending on the voice.
You may be talking about binaural recording.
From the Wikipedia
Binaural recording is a method of recording sound that uses two microphones, arranged with the intent to create a 3-D stereo sound sensation for the listener of actually being in the room with the performers or instruments.