Both the patent and copyrights gives the exclusive rights to the holder. Sometimes if a scientific work is invented, if published in a journal it goes to copyright and if the author files a patent it goes to patent.
Copyright covers literary and artistic works (writing of a book, article, computer code, sculpture, piece of music, etc.). It covers the expression of the work. The patent, on the other hand, cover the protection of an artifact, method of production, chemical composition, etc (i.e. invention).
Where there might be some commonalities is in the concept of a design patent. Though the design patent covers a particular cosmetic aspect of an object that has some practical utility (for example the shape of the mobile phone that has a particular grip design that is cosmetically appealing )