When speaking, I hear my own voice very differently from how others do and from what it really is. The sound differs in tone, pitch, volume, etc. For example, recordings of my singing or speaking in foreign languages sounded a lot worse than what I heard in my own head.Is that a popular phenomenon? Or is that a syndrome, and which parts of sensation and perception are unusual? Last, is it modifiable? 
Why does your recorded or objective voice sound different to what you hear in your own head?
cognitive psychology;perception;sensation;hearing
I think this is not a psychological syndrome but just a reflection of the physical procesces. As such it might not be on-topic for this site. Having this said, here is a quick answer.When you hear your own while speaking, the sound source is in a different place than it is, when you hear a recording of your voice through a loudspeaker. In addition, when you hear your own voice while speaking, you not only hear the sound that is in the air, but you also have the vibrations from within your body, which is an additional sound source. Others dont have the additional source. So these two factors alone make for a very different sound quality.Besides, not every recording of your voice sounds the same. Now, I am sure there are a lot of psychological processes at work, when your hear a recording of your own voice. Unfortunately I don't know about these. But for example the position of the microphone will greatly affect the sound of the recording. Any musician who has tried to record himself will attest to that.I wouldn't be so sure, though, that the recording sounds worse than your real voice. That's probably just a your subjective perspective. I also found it interesting that you talk about how your voice really is. I think that the sound of your voice that you hear while speaking and the sound of your voice that others hear when they listen to you are both instances of your voice as it really is, just from different perspectives, whereas on a recording you could actually change the sound of your voice by means of a lot of different sound effects.