Copyright infringement involves the unauthorized or unlicensed copying of a work that is subject to copyright without obtaining the copyright holder's permission.
Plagiarism is using someone else's work or ideas without giving the creator proper credit (i.e. presenting their thoughts, words, or ideas as your own).
While plagiarism is an ethical violation by academic standards, it is not illegal. Copyright infringement, however, is illegal, as it violates the legally protected rights of the copyright holder.
It is possible to be guilty of either plagiarism or copyright infringement in various situations, but it is also possible to be guilty of both at the same time. For example, if you were to copy the lyrics of a popular song and post it to a website, claiming credit for the work, you would not only be guilty of plagiarism (by passing off the lyrics as your own words), but also guilty of copyright infringement (by copying and distributing a copyrighted work without permission of the copyright holder).
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