Miriam-Webster defines these two, often interchanged, words in our common vocabulary.
belief - [1] a state or habit of mind in which trust or confidence is placed in some person or thing; [2] something that is accepted, considered to be true, or held as an opinion; [3] conviction of the truth of some statement or the reality of some being or phenomenon, especially when based on examination of evidence
faith - [1] loyalty or allegiance to duty or a person; fidelity to one's promises; [2] sincerity of intentions; complete trust; [3] believing with strong conviction
Belief is taught or acquired by external and outer experience. Faith is nurtured and grown within and internalized.