The difference is that the evidence is there, published, made public and available to anyone that wants to see it.
That the evidence is there does not impact how the person who believes in it does so.
You can look at a tv and believe it is possessed by demons that use images to enchant and confuse us if you like, but the evidence is there to show you how they really do work if you choose to look for it.
First, as I've mentioned, most people will never choose to prove every scientific principle which impacts their lives. They take it on faith that it does work and move on. It's a good model in general - we haven't the time (and some of us haven't the education or even the intellect) to prove everything is true before believing in it.
What you're talking about is a relationship between belief and objective reality that may not exist - and it certainly does not have to exist.
A person who has never seen a television before may well think it is full of small people, but they choose to believe the evidence of their own eyes that it works.
A person from a more modern society may believe that there are scientific principles that govern how a television works but not understand them.
Another person may have an engineering background and understand very well how a television works, right down to the basic theory.
Each of these persons has a different personal understanding, and a different personal belief. But the television works regardless of how they feel about it. Their belief is completely decoupled from the objective reality.
If I use your logic, the person who had never seen a television before and believed that there were small people in it would
not be engaging in an act of faith, because even though their belief was wrong, there was an objective reality - that television works - which vindicates his belief that it does indeed work. In other words, if the technology works, regardless of how you think it works, then it is not faith.
If that is the case, then a person who believes in a particular religion is
NOT engaging in faith if it turns out somehow that his particular religion is true. But since he does not know that today - nor do any of us - I submit that he
is engaging in an act of faith. It will stop being faith if his God pops up and shows us all the incontrovertible fact of His existence. He does not engage in faith because there is no proof of his God's existence, he engages in faith because he personally has no such proof. Whether his God exists or not is beside the point of his belief.
I say the primitive man is engaging in faith because he does not understand how the television works, regardless of the fact that it does work (but due to a different principle than little people inside the box).
Likewise, the person who understands that televisions are based on scientific principles but does not know how, is also engaging in faith. His understanding may well be faulty, although it is probably not as off-based as believing in little people inside the box.
It is not the objective reality which makes a person's belief 'faith'. It is how they understand it.