They are the same thing. In the UK we often talk about stammering whereas many other countries talk about stuttering. The sounds you mentioned, D and P, are examples of plosives. Other plosives include B, T, K, G. There can be more tension in the mouth/lips when producing plosives because the tongue/lips fully come together for a moment and air pressure builds up. Vowel sounds are also often tricky for people who stutter (I find words that start with vowels difficult in particular).