A quirk in copyright law means that it is relatively cheap and easy to obtain the right to record a cover version of a song. The copyright holders of the original version may not deny you a license to record a reasonably-similar version, at a rate regulated by law. You might even be able to negotiate a lower rate! In contrast, there is no compulsory licensing sceme for samples, clips, or substantially modified versions of songs. This means that it might be much more expensive to license a short clip from a song than to record and release a cover version of the entire song.

Copyright laws would allow a lawsuit for plagiarizing a song and refusing to pay royalties, although U.S. law allows for exceptions under limited circumstances, such as including portions of the copyrighted material as part of a published critique, often called "fair use".  In addition, you may not need to pay royalties or obtain permission of the copyright holder if your version of the song is a parody of the original, such as might be performed by "Weird Al" Yankovic.

Because when you ar coveing a song you are naming who wrote and compsed it. You are not pretending you wrote it yourself. Plagiarism occurs when you claim as your owna song from sombody else (or it looks similar enough...) same with plagiarism in academai.