First I think in the play,the timing of the shrew. Kathrina, who is the sister, strongly reject what her father had tole her. Her father wants her to get marry but she doesn't. She is just showing her own personality that she doesn't want to follow what her father had told her. In the movie,10 things that I hate about you. The sister which is Kate didn't follow what her father had told her either. But she did it on a different purpose. She had been hurt by a guy before, and this makes her can't trust any boys any more.
The second differce that can be shown in these two stories is about the younger sister. In the play, the younger sister, Bianca, doesn't really care about what her older sister is doing and what is her feeling about having a relationship. But in the movie, another Bianca, which is the younger sister, actually did care about her sister, Kat. She wants to go for a date, but her father doesn't let her to date with anyone. So the dad made a rule, she can only date once Kate dates. And Bianca actually communicate with Kate that it is not a bad thing to try another relationship.
The third difference is that the father in the play doesn't really want Kathrina to be staying with him. He is trying to get rid off Kathrina and that's why he is keep setting marriages for her. But in the movie, the father just wants to protect his daughters. He doesn't want them to get pregnant before they get married. He thinks that having a relationship during a high school educationing process is not a good idea.
These two stories have basically the same situations but some different view points. But still it is hard for a father and a daughter to have the same idea in their mind. It is really fun to see how a father works with his own daughter when his own children is not doing what he told them to do.