The difference between Trump and Clinton - when it comes to "truth" is simple - its about managing expectations.
With Trump - his image, and thus his expectation, is that of a testosterone-driven, bombastic, in-your-face, grab the world by the balls type of attitude. His image is that he will stand up to everyone and make them bend to his will. For better, or worse, a lot of people like that attitude, and want that type of leader.
Clinton, on the other hand, is trying to portray herself as the adult in the room. The one who will take a broader look at things and not go rushing in, rather taking a considered approach when dealing with issues, looking at a problem from multiple points of view. A lot of people like that.
When Trump lies - its mostly bravado - and feeds into his image. We expect a person like Trump to lie and brag alot - so when it happens we are not moved. We are not disappointed, instead we nod our heads, and think "Trump is who we thought he was" His supporters would lose more faith if he told the truth than if he lies....
When Clinton lies, it tears down her image of being the adult in the room. We hold her to a higher standard - because she holds her self up as being the most prepared candidate in the history of ever. When she is caught in a lie - we think its a calculated parsing of the truth. What else isn't she telling us. If we can't trust her, what else does she have going for her? Will she really take a considered approach - or is she lying about that? Will she really look at multiple view points, or is she lying about that?
Its not fair - but the candidates have defined themselves this way, and ironically they have defined their opponents this way.