Faith is the infant child that knows Mummy is the source of all good before it knows what is mother(hood) or even how to say Momma!
IOW faith is pre-emotional, pre-intellectual; vivid vivacious vivifying, close to the source of life itself.
Belief is the ossification of faith; a half live half dead thing which has its own peculiar not-so-pleasant smell.
At the deepest level, faith is inevitably faith towards the source of life itself. Theists may choose to represent this source as The Source – God – but it can be seen in non-theistic, non-religious contexts such as when someone puts up a heroic fight against a terrible disease or adversary.
While it often is based on a theistic orientation or the adversity generates so called religious feeling this is not necessary; it could be something more elemental – Schopenhauer called it Will to Life. Where does that Will originate? The faith that life is good to live however seemingly locally bad
Children naturally have few beliefs and strong faith. That's the source of their vivacity
But any strong and successful person – say a rags-to-riches story – will invariably be seen to have a faith in their idea their wish, ultimately faith in themselves.
And as that faith hardens into fixed patterns - ossified beliefs - it loses its power.
Heck the very engagement of questioners and answerers here requires the faith that there are reasonable decent humans on the other side, – we are not failing some Turing-test with a bot! – asking/answering "in good faith".