This is a tough one. They are sometimes used interchangeably, but they are not the same.
When something that you believe is disproved, you no longer believe it. Simple enough. Not so with faith; faith is "shattered" or "lost." On the other hand, faith cannot be proved or disproved. You have it or you don't, but it can be shown to be neither valid nor unjustified. That is why, when testing my own beliefs and my own faith, I can find my beliefs to rest on shaky ground, while my faith remains strong. There is a growing gulf, now a chasm, between the two for me. CLEARLY, I cannot continue to believe what I have always told myself I believed. But just as clearly, I know God created and set things in motion.
Did I ever believe it? Doctrine, along with the process of indoctrination, is both a blessing and a curse. They are employed for good and for evil. Humans are uniquely susceptible to, and exploitable by, such forces. They require you to say "I believe" until you reach the point that you actually do, or at least convince yourself that you do, because really, you should believe, shouldn't you?
Hopefully people can be honest enough with themselves, after enough soul-searching, to know that if they really don't believe something, then merely reciting the words does not fool God. Creeds don't leave wiggle room; they don't allow for individuals to customize exactly what they really do feel. Everyone needs to believe the exact same thing, because those who know best - well, they know best. But when one doesn't even know exactly what every word means in the native tongue, how could he or she possibly know what the original words and expressions in Ancient Greek conveyed? The Early Fathers of the Church, from Alexandria and Jerusalem and Rome and Damascus and Byzantium and Lyon, may have known exactly what they believed, but it's profoundly unlikely that their exact intentions in their varied languages have been completely passed to me in English.
So do I continue to recite the creeds, to set an example for my kids? I may be wrong, after all, in my faltering belief in Orthodoxy. Yes, I do continue. And I raise them to explore, to search, to know themselves, so that one day, they will be spiritually and mentally strong enough to believe what they know and know what they believe. And I'll leave it up to God to instill them with the faith that no creed or religion can instill, no matter how many years of ritual and devoted practice they go through.