As the previous post stated the word, "catholic" means universal. So, the catholic church is claiming to be the uinversal church.
When we add the adjective, Roman, we are referring to one expression of Christianity. Currently there are three major branches and at one point, there was a fourth: Catholicism, Orthodoxy, Protestantism and the Syrian church.
In terms of the beginning of the church, there is no one answer. So, let me give you a few different perspectives. First, some people will say that the chuch existed in the Old Testament, since they had faith in God. For example, they say that the assembly of God's people in the Old Testament equals the church. Second, some people will say that the church started with Jesus' ministry and his promises to build his church (Matthew 16). Third, others will say that the church came into existence through the works of the apostled who were commissioned by Jesus to establish his church (Ephesians 2:20).