If I understand your question correctly, you are asking as to why what you hear from a microphone recording or PA System does not sound like the original voice.
There are many reasons, but the most important is that the equipment is actually changing the sound. The microphones, the amplifiers, and the speakers, all have an effect on the sound. Even the best equipment leaves some impact.
In the case of human voice (recorded in a quiet setting), there are a few major factors.
1) Microphone frequency response.
Microphones are not as sensitive to some frequencies as they are others. This means that some microphones might make high pitched sounds seem much louder than low pitched sounds, even if they really should have been at the same volume.
2) Distortion, coloration, or noise from the amplification unit.
When you record something, or when you speak over a PA system, the signal needs to be amplified somehow. This process will usually add 'harmonics' and 'distortion' that result in the nature of the sound changing. Think of the sound of a typical electric guitar solo, compared to when the guitar is unplugged. This is an example of extreme coloration and distortion from an amplifier designed to add as much character as possible. Amplifiers for recording are usually designed to add as little coloration as possible. The good ones are expensive though, and still change the sound a little.
3) Frequency response of the speakers.
Just like how microphones have a frequency response curve, so do speakers.
This means that some speakers will make high pitched sounds louder than low pitched ones, and visa-versa for others. Good quality professional speakers (called monitors) will try to make all sounds equally loud. Some cheaper ones might try to make the bass extra loud, in order to be 'cool'. You've probably seen that you can adjust the bass/treble ratio on most stereo sets, this is to compensate for the limited accuracy of frequency response, and allows you to change it to your preferences.
One other thing. You may notice voice recordings of other people sound closer to the original than recordings of your own voice. You might think that it's just your imagination, or that you have somehow recorded the voice wrong, but that's probably not it. It's actually because you don't hear your own voice the way other people do! When you speak, the sound moves through your bones and into your ear directly in addition to the sound from the air. This means you get a huge amount of bass frequencies and some additional harmonics that are very different from what you hear from the air.
That means the microphone, and everybody else, actually hears something different from what the person speaking hears.
There are a few techniques for trying to emulate this effect though. Like trying to put the microphone closer to your chest, or adding some reverb with a low-pass filter. The room and microphone type also can matter here... The closest I ever got to matching what I perceive my own voice to be, was when I setup an omni-mic in a very narrow but long storage closet, and spoke into the air above the microphone. The result was surprisingly close to what I hear when I speak, and very different from what I get when I do this in a plain old room with no special treatment.