Selective mutism (now more accurately labeled as situational mutism) is not present in most stutterers. The vast majority of people who stutter do not have SM. However, it does happen, and I have worked with a few people who stutter who also have SM. SM is an anxiety disorder and can be mild to severe. It is not a speech disorder, although SLPs are often involved in diagnosis and treatment. There are other more common kinds of anxiety disorders like generalized anxiety and social anxiety. People who stutter who seek treatment are more likely (in my experience) to have an anxiety disorder, but even for those seeking treatment, most do not have an anxiety disorder. What I find is that many people who stutter have higher levels of anxiety than people who do not stutter, but this is not a disorder -- it is a normal response to a difficult situation. It is annoying, frustrating, and discouraging to have your speech constantly or randomly interrupted and to have people react to that in unhelpful ways, and a perfectly normal response to that situation is to feel anxious or depressed. If and when those feelings rise to the level of interfering with your life or happiness, seek help. A well-informed stuttering specialist understands and can help you through both the stuttering issues and the social-emotional stuff.