The gulf between truth and fact is both vast and significant, and it is an indication of our society's poor educational habits that very few people even know that there is a difference. Even worse, many people aggressively avoid the differentiation, mostly because they want their truth to be the one and only truth. To be blunt, facts are objective and truths are subjective.
Facts are those things that are demonstrable and independently verifiable. Facts are based on evidence. An example of a fact is the boiling point of water. Few people would argue that, at standard sea-level air pressure, water boils at 212 degrees F or 100 degrees C. Similarly, the laws of gravity are readily demonstratable.
Facts can have the qualities of being valid or invalid, verified or unverified. To qualify as a fact, information has to be verifiable. If it can never be double-checked, it is not a fact; it is a truth. Scientific method is based on the creation of new facts by carefully connecting a fact with a reproducible method for verifying the validity of that specific fact.
Facts are not readily disregarded by anyone attempting a careful analysis, but it is unfortunately often the case that people would rather have their information be the right answer than have to change their mind due to an inconvenient fact. The more that is at stake for a person, the more likely that person is to disregard facts. As a result, deeply religious people, politicians, and anyone whose power base is dependent on a specific set of beliefs are some of the most likely people to fall prey to this personality flaw.
Truth, on the other hand, is usually information that a person has received from a trusted source, but can also be something that a person develops on his or her own. Truth is based on trust, faith, and belief. Good examples of this are The Big Bang and Creationism, both of which are completely true within the group for which they are popular, and obviously false with "the other" group. As much as we'd like to be able to verify or discount one or the other, none of us was there, so we'll never really know (read Terry Pratchett's book "Strata" for a good example of this).
Since truth can be different for each individual, it is essentially a commonly held opinion. As such, a truth can never be true or false, right or wrong. It can only be popular or unpopular, founded or unfounded. This vexes a lot of people because they hang their ego on their truth not only being the only truth, but being "right" with the authority of a higher power whose existence is also merely an opinion.
This mentality has caused many wars where people try to force others to accept their truth as a fact, and it continues today in the form of various holy wars, factional in-fighting, gay-bashing, evidence tampering, and election fraud. It is amazing how often a governmental body passes a law simply to state that their opinions are the "right" opinions. Most "congressional resolutions" are in that vein. People's willingness to persecute others in order to get them to change their minds is extremely well documented throughout history.
Exercise: How well can you differentiate fact from opinion? List ten pieces of information that you consider factual. Write them down on a piece of paper or type them out. Don't read the rest of this article until you have all ten listed. This won't take much time - most people can dig up ten facts off the top of their head in no time at all. Stop reading this paragraph if you haven't completed your list of ten facts. You will change the results if you keep reading without that list. I often read through an exercise to see if it's worth my time even if it tells me not to, but if you're going to do that then you might as well not even bother doing the exercise at all because it really will skew the results beyond repair.
Is the list complete? Whew, good. Now figure out where you learned each of those ten things. If you can't trace a piece of information to a reproducible example or a defining authority (there are a thousand millimeters in a meter because ANSI says so...) then it is a truth. Even something that you feel certain has to be a fact is really only a truth unless you can trace it back. For millennia, people thought the flatness of the earth was a fact, but it could really only be traced to the idea that it was obvious or common sense. Religions were very much in the habit of killing people who insisted that the earth was anything besides flat.
Do this exercise regularly, and you will learn a lot about the world you think you live in.