She says she never sings and dances in public, but back in high school she did sing and dance in the school 和 She says she never sing sand dances in public, but back in high school she did sing and did dance in the school 的差別在哪裡？如果不好說明，請提供一些例句。

In both sentences, you should take away "the" at the end (so it becomes "in school"). Aside from that, both sentences are grammatically correct (though you made a simple typo on the second one: "sing sand").

The first one probably sounds a little more natural, but it doesn't emphasize dancing as much as it seems you want it to. If you want to drive home the emphasis that she did both things, you could say:
"..., but she *not only* sang, *but also* danced in school."

This is a very common structure: "not only X, but also Y"