This may be my Chinese getting in the way of my Japanese again, but doesn't 体育 and スポーツ both mean "sport"?
What are the differences between them, and when is one used over the other?
体育 is physical education, a class taken at school where students exercise and play sports.
スポーツ is sports in general, including professional sports or sports played as a hobby.
体育 ＝ Physical education
スポーツ = sports
(I don't know Chinese but I am curious, is your Chinese getting in the way?)