Sometimes they are used interchangeably, but there are some differences. As far as I know, both stutter and stammer exist and describe the same speech dysfluency is because stammer is a mostly British term, whereas stutter is largely used in the US, and New Zealand and Australia. Some definitions describe a stutter as the repetition of letters, whereas a stammer is the blocking and prolongations but I don't think most people make that distinction.

To my mind, someone HAS a stutter. That is, a problem with their speech that causes them to repeat the beginning sound of a word more than once before they can say it. Stammer is more of tripping over your words because you are nervous or scared. As the person above me said, however, most native speakers use them interchange.