The word catholic means universal and once upon a time there was only one universal Christian church, and its headquarters was in Rome, because of the influence of the Roman Empire. ALL Christian denominations are offshoots of the Roman Catholic Church.

For starters,Catholic capitalized refers to the actual Church, while the word catholic lowercase means universal. However, I believe you are asking if a Catholic church and a Roman Catholic Church are the same thing: they are. These days, people use the terms Catholic and Roman Catholic interchangeably. The phrase Roman Catholic simply is a reference to the fact that the Church leadership is based at the Vatican.

The term "Roman", attached to the correct label of Catholic, began in about the 15th century. During the Protestant reformation, the addition of "Roman" to the proper and correct term "Catholic" was generally intended as an insult. Eventually the insulting insinuation sort of fell away, and the term is widely used today to denote Catholics who are obedient to the Pope in Rome, as opposed to eastern Catholics, who reject the authority of the Pope. In the "Oxford English Dictionary", which many consider the highest existing authority upon questions of English philology, the following explanation is given under the heading "Roman Catholic". The use of this composite term in place of the simple Roman, Romanist, or Romish; which had acquired an invidious sense, appears to have arisen in the early years of the seventeenth century. For conciliatory reasons it was employed in the negotiations connected with the Spanish Match (1618-1624) and appears in formal documents relating to this printed by Rushworth (I, 85-89). After that date it was generally adopted as a non-controversial term and has long been the recognized legal and official designation, though in ordinary use Catholic alone is very frequently employed. (New Oxford Dict., VIII, 766)