Why do some people not stutter when they act on stage or perform?

Why do some people not stutter when they act on stage or perform? I've always loved musicals, acting and singing from a young age, but I always thought my stutter would keep me from acting in any capacity. I decided to audition for my schools musical last year on a whim. Im not going to lie... my singing skills are there, but Ive never acted. We were doing the Wizard of Oz that year and I soooo badly wanted to be the lead. Im an attention whore, what can I say? But the audition went well. I'd never spoken to the director previous to the audition and I was not looking forward to her thinking I was nervous just because I stuttered. But when I was reading my lines, I just... didn't stutter. This was one of the only times in my teenage years I spoke 100% fluently, at ease, relaxed. I got the lead. That 1 matinée and those 3 night shows I did later that year were probably the best experiences of my life. 2 hours on a brightly lit stage, no stuttering, singing my heart out and finally a huge round of applause. It felt really good and Im so glad to have found this outlet to express myself and just let go of any tension or negativity. Ever since this experience I've been more fluent - life has become my stage, sort of. Anyway, back to the point Im trying to get to. I remember in the first rehearsal we ever had, she noticed I'd stuttered a bit in conversation (a bit? She was being polite I guess. My speech was probably the worst it had ever been at that point in time) and asked me about it. I told her I had a stutter. She was really shocked but began asking me a lot of questions as to WHY I didn't stutter on stage. I... I didn't know. I felt almost ashamed to not know... I mean, stuttering has become an everyday thing. How could I not know this about myself, and why had I not found out about it sooner? So I'm really curious but never looked into it. why? and why do so many stutterers seem to feel the same way about this? Id love to hear some ideas :)