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.
There are far more differences than similarities between the two. Roman Catholics as Christians believe that Jesus was the son of God. Muslims believe that Jesus was a great prophet sent from God; but his message was rejected; therefore God sent another, final prophet, namely Muhammad. Roman Catholics believe in the Trinity of God the Father, God the Son, and God the Holy Spirit. Muslims believe, as stated in their creed that there is no God but God. The God of Islam and the God of Christianity are one and the same, although many fundamentalist Christians attempt to deny this. Both believe in reward after death for a righeous life and punishment for sin. Both also believe in the importance of a number of Old Testament figures, primarily Abraham, who is believed to be the father of both Jews and Muslims. Catholics fast during certain days of Lent; Muslims fast during daylight hours during the Holy Month of Ramadan. Finally both consider the land where Jesus was born as holy, a major cause of the Crusades.