As a matter of fact, all three of them - Aurelia, Catalina and Louis - are half-siblings. They are not, however, step-siblings. Let's keep in mind that all of them are children of the same father, Charles. However, Charles never married any of the women mentioned. That is, he never married Cat's and Louis's mothers. Therefore, there is no "step" in this. However, even though the children's mothers are all different, they still have Charles's DNA. That makes them half-siblings. Having that in mind, we can easily say that Louis is Cat's half-brother.
Both of the stories are about brothers that one of them take advantage of the other ones and they all fight. Shakespeare’s is a little more light hearted then the other one and there are many different aspects to it that make Shakespeare’s light hearted like how they are constantly calling each other names.