When I sing/hum lets say C note and then play on a piano a C note too, the sound I hear overlap so that I can immediately know if its the same note or not.
I want to know if everyone can do this and why does the sound overlap?? if it does overlap because its the same note, why cant I hear that overlap when I play the same notes on piano, but only when I sing/hum the notes.
Playing a note and simultaneously singing the same note is something most people can do, although there are some who are tone deaf and cannot sing the same note they hear.
Your question, though, is about something else. When you play two notes of the same name, on a piano, they must be at least an octave apart; pianos don't have the propensity to play two separate notes in unison, only in octaves. So, you're not hearing the same thing as you do when you play a certain note and sing it, at exactly that pitch, at the same time. Thus, the two effects won't be the same.
No, not everyone can do this (although those who can often have a hard time imagining that anyone might not be able to).
For instance, one of the tests often given to prospects for military recruiting is how well they can distinguish tones of grossly or slightly different pitch. This is supposed to indicate how well they would do e.g. at signal communications jobs. (Needless to say, musicians are also almost exclusively recruited from people who are good at it.)
