Stuttering and Stammering have the same meaning - It is a speech disorder in which the person repeats or prolongs words, syllables or phrases.
The person with a stutter (or stammer) may also stop during speech and make no sound for certain syllables.
People who stutter often find that Stress and Fatigue make it harder for them to talk fluently, as well as situations in which they become Self-conscious about speaking, such as Public speaking or Teaching. Most people who stutter find that their problem eases if they are Relaxed.