The best way to understand truth vs falsehood is to learn from the second richest man in the world: Warren Buffett.
Not only did he become rich (he was the richest man before the arrival of Bill Gates on the scene), he did so by searching for the "truth." His investment advice, in fact, is always full of moral lessons to be learned.
He searched for the "truth" by separating information into 4 categories:
1. What's important and can be known (integrity of the people you work with; their intelligence and values and energy)
2. What's not important and can be known (facts, data)
3. What's important and cannot be known (the true feelings of a CEO, his true motive)
4. What's not important and cannot be known (astrology)
By focusing on information in category #1, you will be able to find the truth and use it.
2, 3 and 4 are various degrees of falsehood.
Regarding #2: the news media may report facts, so they are factual. Reporters live and die by the accuracy credo: they must only report facts.
Yet, in a way, what they report is false because it is always a certain angle that is being reported.
It's like showing people the tail of an elephant and claiming that you are showing the truth.
Indeed, a truth is a global fact whereas a fact is a local truth.
I think this relationship between truth and fact is more important than the relationship between truth and falsehood.