Singing for yourself at home is something you tend to do at less than full volume which means, in my case (ignoring other changes due to age etc.) means I tend to sing a couple of tones too low. Up on stage, especially if there's no PA, no matter how good the acoustics are, a higher pitch allows the voice to carry better, at least in my experience. The downside is that all those beautiful accompaniments tend to be write-offs since all too often it's not simply a case of capoing up or down.
My speaking voice can be a problem- I'm a voice-over artist and quite often if I'm close to the mike and speaking fairly quietly the pitch slips a tone or two upwards in the direction of the 'Head voice' rather than the more usual, and usually required, 'Chest voice'.