Anthropomorphism means attributing human emotions and motives to animals (especially) and to objects. It is generally used with a slightly negative connotation to show the user finds some remark or behaviour inappropriate: you might describe the remarks "that turtle looks so sad" or "this computer is just trying to frustrate me" as anthropomorphic. (The word also has some religious applications that I won't go into.) "Personification" in contrast usually applies to abstract concepts taking some human form: e.g. Hitler as the personification of evil, Marianne as the personification of France, etc.

The definition you gave also applies to "personification" and so the two words are synonyms. However, "personification" has a second meaning of "embodiment" which refers to when an abstract concept takes or assumes a bodily form e.g. "The receptionist at the Dorchester Hotel is the personification / embodiment of charm when greeting guests." This means that he is so charming that if charm had a human form, he would be that form, he would be charm itself. It's obviously a literary way of speaking.