Plagiarism is to misrepresent something as authored by yourself. Whether you paid someone else for writing it or copied it without permission does not matter for the plagiarism charge - the wrongdoing is the misrepresentation.

It is not the same as copyright infringement - although it might be both at the same time if you copy something without permission and publish it under your own name.

Plagiarism is not always illegal. Publishing a book which is ghostwritten by someone else is not illegal AFAIK (as long as they get paid). But in education and research it is illegal - and they don't care if you bought the material fairly, the point is that decisions (grades, hiring, funding etc.) are based on the assumption that the material reflects your abilities.

So it is not really "theft of ideas", it is "faking credentials".