What you hear when you speak to someone or when you sing for someone is the sound going through the bone in your head. This is different when you are listening to your own voice through nearfield or midfield speakers. In short, the aforementioned phenomenon is called bone conduction.
In addition, the type of microphone (i.e., condenser, dynamic, or ribbon microphone) you use plays a significant role in the end result. Don't forget the quality of it too. Not all microphones are the same even though they may be of the same type. Their frequency response will always be different from one manufacturer to another manufacturer's specifications.