There are two major similarities between these two religious faiths. First, they are both monotheistic religions, believing in only one God. Second, they both believe in the divine inspiration of some of the same scriptures. Roman Catholics believe in the Old and New Testaments. Muslims believe in those scriptures as well, but also believe that the Koran is divinely inspired and is not corrupted the way that the other scriptures have become over the years.
There are many differences. Perhaps the biggest one is that Muslims do not believe in the divinity of Jesus Christ. More specific to Catholicism, Islam does not believe in creating representations of holy people. By contrast, Catholic churches have many statues and paintings of Jesus, Mary, and various saints. This would be seen as rather sacrilegious by Muslims.