The Taming of the Shrew obviously has a more central focus on the importance of marriage because of the social expectations during Shakespeare's day. Marriage was the appropriate 'sphere' for the woman, and Kate and Petruchio's relationship explores how a strong-willed woman like Kate can find her own identity through the marriage relationship.
In Ten Things I Hate about You, the focus of the movie is not about marriage, but rather the rules and social expectations of couples when dating, since the characters are modern high school students in California. The father figure emphasizes the importance of his daughters not dating, because of his fear of teenage pregnancy. Bianca cannot have a boyfriend or date until her reluctant sister Kate chooses to do so. In this adaptation of Shakespeare's play, Kate struggles to align her strong, feminist attitude with the possibility of romantic love.
Both Shakespeare's play and the film examine the societal norms of their corresponding time period and address how both women and men adapt to social expectations. Whether the focus is marriage, like in Taming of the Shrew, or dating, both works ultimately prove that the individual must pay heed to social expectations while staying true to themselves.