May I suggest another definition of 'Faith'?
In my definition, faith is a lack of the desire to measure and to judge objects as one does not understand himself as a separate subject. This in turn leads one to a certain detachment from conventional life, taking it not all too serious anymore.
It doesn't mean that one stops entirely to measure and to judge, but one stops in taking it entirely serious. When one has faith, he starts to see it more like a game.
So, as for me, its always quite a sure sign that one is lacking faith, when his ways are not playful but all serious. And that's why there is no faith in all the churches of the world, because nobody of them really religious people dares to laugh when facing the altar. That's what makes faith different from believe. That's why I consider scientists, that can not laugh into the face of their theories, taking it all seriously, as religious people. As well as atheists, that take their believe in the non-existence of god dead serious and thus regularly engage in zealous debate with the theists, which again are seen, quite undeservingly I think, as the archetype of the believer. Because the fact that the theists were the first to believe, before all the other '-ists' could join them, doesn't necessarily mean, that their belief is somehow more fundamental.
It's the laughing at idols in all their manifold forms that separates faith from belief. And that's why defining things is strictly speaking a lack of faith, above all when they are taken seriously by the definition maker. So when stretching things a little, we could say that 'Faith' and the Paradox', the 'Absurd', is one and the same thing.
Thus it is not all that surprising that faith and believe are confused all the time. Since, on the other hand, there is no sure sign for faith. When one is all playful and not at all serious, that's not a sure sign for faith too, because chance is that he's just a clown. Ever heard of the sad clown? Faith therefore is very difficult to discern in other people. And it's not possible at all to discern faith from belief by just knowing the surface of people. That's why it is so easy to pretend and put a great show on. That's why it is so commonly institutionalized into churches of all kinds, because it's a con that is so easily pulled of. Churches basically are a con act institutionalized. People go to church not because they are faithfull but on the contrary, because they lack faith and thus believe it's a serious and very important thing. Look at the churches and cathedrals. It is very important that they are superior to everything else, that's because it is such a serious thing.
As I see it, faith can only be noticed in people that are very close. And even then it is very difficult. And people are not static. But the good news is that it is much easier to discern faith, or the lack of it, in oneself than in others. Because if you are going to take an exam and as a result are very nervous and sweating blood, it's clearly because you are lacking faith and thus believe that the result of the exam really is no laughable matter.
If belief is the illness, then faith is the cure.