The Latin Rite has always had a diversity of rites in it, meaning that the Mass in each of these rites had its own peculiarities. In addition to these are the various rites of the Eastern Church in union with Rome. These Eastern Churches are as Roman Catholic as the Latin Rite and its various "rites." You can read about the various rites by PRESSING VARIOUS RITES HERE.
In the Latin Rite even more diversity is becoming acceptable and not causing a blink of an eye. The legitimate return of the "unreformed" Mass, known as the Tridentine Mass and now the Extraordinary Form Mass may be celebrated without permission from one's bishop thanks to Pope Benedict. So many parishes today celebrate both the reformed Catholic Latin Rite Mass, known now as the Ordinary Form (regular, usual) and the Extraordinary Form to meet the pastoral needs of one's parish community.
In addition to this, the pope has allowed and is allowing the development of an Anglican Use Mass based upon the liturgies of the Anglican Church, known here in the USA as the Protestant Episcopal Church. Episcopalians and Anglicans can return to the full communion of the Catholic Church and maintain their "patrimony" of liturgy much of it going back to the time when the Anglican Church was still in full communion with the Pope. King Henry VIII's separation from the Church of Rome initially maintained all that was Catholic until he killed off the Catholic hierarchy loyal to the Pope and the Protestant Reformation began having a deleterious effect upon the Anglican Liturgy and its sacraments, including validity of Holy Orders and thus Confirmation and the Holy Eucharist.
Eastern Rite Catholic Church showing Iconostasis, behind which is the altar
Eastern Rite Catholic Byzantine Liturgy
Anglican Use Rite for Benediction also showing the Rood Screen which comes from the Eastern Rite Iconostasis
Extraordinary Form of the Catholic Mass
Anglican Use Rite of the Catholic Mass
Ordinary Form of the Catholic Mass