There are uses where they are synonyms. "This test is tough." "This test is difficult." However, there are many cases where they have different meanings. "My mom is tough." means that she is a strong person, either physically, mentally, or emotionally strong. "My mom is difficult." is generally a negative thing to say, as it means that she is difficult to deal with. It probably means that she is stubborn. It's best to learn words in context, and not from a dictionary, because dictionaries can lead you astray. A good dictionary is one that has example sentences for every different use of a word. Study the sentences first.

Tough can have a physical meaning as well. It's not possible to say, "This steak is overcooked. Its texture is very difficult." Also, "a tough person" and "a difficult person" mean very different things.