Person who stutters became the term of choice because you're not just a stutterer. A lot of pws do live with that as their core identity but there is so much more to them, just like there is more to any person than one adjective. You're not a stutterer, you're u/lullbobb555. You do this and are that and you also stutterer as well. I call stuttering a communication disorder (you can use speech disorder if you'd like). There are plenty of people who stutter you won't actually actually hear stutter. They either block and don't say a sound until they feel they can get it out fluently. Or they hide it altogether through word substitution and avoidance. I'd honestly say the physical impediment is the smaller part of stuttering.