Taking just means, broadly, “to gain or acquire”. Repetition of an incorrect point doesn’t make it any more valid I’m afraid.
Copying is often called taking a copy. Even basic usage of the term copying invalidates your point!
As for “not allowed” that will vary by contract/law/agreement/license/etc
This distinction is why it’s usually not downloaders that are punished, rather uploaders: they’re the ones that broke an agreement.