no no no.
you believe that those are what these words mean because the dictionary says so, no?
i say, who's to say that the dictionary is even right? those words are extremely difficult to discern for most people. to say 2nd grade is a vast oversimplification. a 2nd grader would just equate the two words as meaning identical things, and that their meaning is "what people told me is true". which is of course incorrect.
simply put:
Truth is what IS. it is independent of all opinion and viewpoints.
Fact is the collected composition of what is believed to have happened/happening/will happen etc. It depends on the opinions of those who collected the information, and is accepted by others based on trust in the integrity of said collection.
example: a car drives by.
there is only one actual event.
however, every observer sees it slightly differently, and if you were to ask them what happened, they would all describe similar but different situations, and then collectively conclude what happened based on the sum of their views. other people would then accept this event's validity based on trust in the collective integrity of those who report it.