这件毛衣不旧 vs. 这件毛衣不是旧的

[Alchemist]

My Chinese grammar says that the two sentences in the topic have slightly different meanings, in that “这件毛衣不旧” describes the condition of the sweater, whereas “这件毛衣不是旧的” is used to explain that it belongs to the category of new sweaters. Actually, I can't think of two different contexts where one of these sentences is appropriate and the other isn't.

Another similar example from the same grammar book is this: “姐姐教书” vs. “姐姐是教书的”.

Can anyone please explain the differences between these sentences? Thank you!

[Quest]

I feel like 并 is missing in the sentences. Anyways, they both sound the same to me. If you want to say "category of new sweaters", you can use 新款。这件毛衣是新货，并不是旧款的。

这件毛衣是新买的，并不旧。

[Quest]

“姐姐教书” vs. “姐姐是教书的”.

My sister teaches.

My sister is (adjectival: one who teaches).