There are many reasons that someone’s voice sounds different when it is recorded. Most notable is that when we speak we are hearing vibrations from the act of speaking as well as what was spoken and when listening to a recording we are only hearing the vibrations of what was spoken and not the act of speaking. All vibrations are creating sound where intended or not.
The next reason can be the path the recorded sound takes. Your voice will sound different on different microphones, pre-amplifiers, recording mediums, and even on different playback devices. Certain microphones are modeled to accurately represent what is heard by the human ear and some are not. This has something to do with price but also type of microphone and the intended use it was made for. Just because the microphone costs $3,000 doesn’t mean it was made to replicate human voice but there is not a $20 microphone that has sophisticated enough technology to master this feat either. Recording at a volume that is too loud will also cause distortion and give a weird representation of your voice. It is always easier to raised the volume after recorded and very hard to eliminate the distortion after recording is complete. Most pre-amplifiers or recording software have a red line or bar at which distortion starts try to keep the loudest parts of you recording at about 75% of the way to this stopping point to give yourself some headroom.
Microphones also record the ‘Room’ sound. You will sound different if you are very close to a microphone or very far away. And if the room has a lot of surfaces that can vibrate you will hear those sounds too, these also include furniture, other people and basically anything that can reflect sounds. Something called the ‘Proximity Effect’ occurs when someone is too close to a microphone. This gives a booming sound to your voice, which you may or may not want. Saying certain letters produces air that can travel faster than the sound it self giving a popping sound on the microphone as you are being recorded. Pop filters and speaking techniques are used to avoid this.
The best way to figure out if the way you are being recorded actually sounds like you is to have someone else listen to you and listen to your recording. If they are a trained listener ask them their opinion because it is hard to judge the sound of your own voice since you are used to what your own voice sounds like already. Then if you want to make it sound differently you can change any other the items I have mentioned to make yourself sound exactly how you would like.