Genealogy: Is It a Direct Adding Male Descendant?

In luke, jesus's father is joseph. But in matthew, we trace from david through solomon. They all have different fathers and different sons above and below them. So you think there has to be something wrong with this list. And a couple of names that show up, like both of them have sialtil, who's the father of zerubabl. It was really just to say it's going to be not looks so much like he's going to inherit something as to say "This is where he should watch fortur"