The difference is that in English, "coat" is frequently used as a generic term, but "manteau" is not a generic term. I.e., a "manteau" is never a jacket. "Un manteau" is specifically a long coat, extending anywhere from mid-thigh to the ankle; it may be thought of as an "overcoat". "Une veste" is a jacket (also called generically a "coat"), a garment that extends either to the hip or slightly below.
I wish I could get back to the original context. Something about the original correction was confusing. Anyway, the 'and' ('et') seems redundant and doesn't change the meaning in either language. Sometimes Duolingo accepts syntactic variations on the same semantic content and other times it doesn't. It is hard to see what is essential and what is not.