This question having spent years studying this very aspect, it would depend on whom you asked....
The reason being is due to the nature of the religious beliefs, being defined as being the faith.
So Christians based on Paul's teachings, would say that 'the faith' is believing the religious doctrine he puts forth....A lot of the other religions have then continued this misaligned train of thought.
If we separate the misconceptions about the word faith meaning a religion, or a religious belief, and apply it in its original context, then your question answers its self.
Faith originally means to trust, it doesn't originally have any religious contexts applied to it.
So a mountain climber can have faith in his own abilities; if he climbs with another climber, then he has faith in their abilities.
So religion doesn't need to have anything to do with faith; faith is a feeling/energy from the heart that everyone has, some more than others.
A religion is a set of fundamental beliefs, that a group of people believe in.
Religions generally tell people to put their trust/faith into their religious belief, as that will then give them a sense of security....
Yet that often leads them to more instability if challenged over their religious beliefs, as they see that as being their heart/faith that is being attacked.
One's religion is a set of fundamental beliefs and practises.
One's faith is the trust and energy from the heart, that allows them to overcome fear.