What is the difference between faith and belief?

There is no difference between ‘faith’ and ‘belief’ — they are the same thing.

Although the words are different in English, the New Testament, for example, only has one family of words (from the root peithō (Strong’s #3982) in Greek) that are translated as both ‘faith’ and ‘belief’.

Part of the reason why the Greek (in the New Testament and Hebrew in the Old Testament) words are translated as ‘faith’ or ‘belief’ is because  English doesn’t have a word ‘faithed‘ or ‘faithing‘, so it has to use ‘believed’ and ‘believing’.

A useful passage to see the interchangeable use of the words ‘belief’ and ‘faith’ is Rom. 4:

{3} … Abraham believed God, and it was counted to him as righteousness.” … {5}… his faith is counted as righteousness … {9} … faith was counted to Abraham as righteousness.

Faith and belief are exactly the same.