Acoustic refers to how the sound is produced. The thick hollow ones that make their own noise. As previously stated, it is the "generic" term that encompasses many different variations.
Classical guitars are a slightly smaller bodied acoustic, and they have nylon strings. Yes, as previously mentioned, all 6 are nylon, but 3 of them have metal windings around a nylon core.
Classical guitars are acoustic guitars. But not all Acoustic guitars are Classical guitars.
If you do not know what kind of specific guitar was used, you are safe to use the general term - Acoustic. But you are not safe to say Classical guitars, even if it has nylon strings.