I agree with radriano that it's no laughing matter for those afflicted. Although that's never been an obstacle to those making jokes... As a pediatrician with a special interest in children with developmental disorders, I'm not a big fan of songs that poke fun at people's disabilities.

By way of clarification, lots of 2-to-4-year-olds (approximately) have what's called "developmental dysfluency", in which they repeat a word or syllable several times. ("My, my, my, my ball is over here.") It seems to come from immaturity in the part of the brain that coordinates thought with speech--as if one track has to mark time until the other catches up. The children seem perfectly unconcerned about it, except when adults try to make them aware of it.

True stuttering, on the other hand, which affects about 1% of the population according to my references, also starts in the preschool years. It generally consists of repetition or prolongation of single sounds, often with excessive muscle tension in the speech and breathing apparatus. Most of the time children who stutter are distressed by it, and the increased effort to control the symptom often makes it worse. It can have a devastating effect on academic and social functioning. The earlier it is recognized and treated by an experienced speech pathologist, the more likely it is to resolve.

As far as I know, stammering refers to any speech problem in which words or sounds are repeated, including stuttering--which is a more restricted term. But usage, like your mileage, may vary.

Aloha,
Mark