The Catholic religion is the religion of the Catholic Church—i.e., that group of churches in communion with the pope. If a group isn’t in communion with the pope, it isn’t part of the Catholic Church.
Within the Catholic Church there are a number of individual churches, sometimes called rites. One of these is the Roman rite or Roman church. It includes most of the Catholics in the Western world. A Roman Catholic is a Catholic who is a member of the Roman rite.
There are many Catholics in the East who are not Roman Catholics, such as Maronite Catholics, Ukrainian Catholics, and Chaldean Catholics. These are all in communion with the pope, but they are not members of the Roman rite, so they are not Roman Catholics.
The Roman rite is not stricter than these other rights. They are equal. They all teach the same faith; it is only local customs that are different among them.