Always sing songs in the key that is right for your voice. Which is quite likely to be different on different nights anyway.

Trying to make the same kind of sound that the person you learnt a song from is never the right way to go. That doesn't mean change it to try and be original and all that, but pitch it the way that your voice requires it, and do it at the speed that feels rigfht, and use the accompaniment or non-accompaniment that helps.

The song is what matters, not the performer.