Within and under the umbrella of Protestantism, there are many denominations. For some Protestants, being a “Protestant” is more important than, say, being a Baptist, or a Methodist, or a Presbyterian. Oftentimes a Protestant will start out raised by his family in one denomination of Protestantism, then explore others as time goes on, to find the denomination that seems to best suit him. Protestants aren’t generally encumbered by our Catholic notion of “One True Church” with respect to individual denominations. For many Protestants, “Reformed Christianity” is the true Church, and anything that they feel authentically holds claim to that term is a legitimate expression of Christ’s Church. So be one a Lutheran, a Southern Baptist, an Evangelical…what you will…it essentially amounts to six of one and half a dozen of the other.
In nowise could Roman Catholicism or Eastern Orthodoxy fit under the umbrella of “Reformed Christianity” from the perspective of Protestantism, of course. The essence of Protestantism is a departure from the Roman Catholic Church, specifically, and by logical extension any Church that clings to the ancient sacraments, liturgies, and doctrines. Some Protestants will not even acknowledge Anglicanism as authentic Protestantism, regarding it as an anomoly existing on its own (Protestants that go to Mass and pray their beads!?!), somewhere between Catholicism and Protestantism (although, in fairness, this is where most Anglicans place themselves).
For Catholics, the paradigm is entirely different. The Church is not a smorgasbord of various denominations, one just as good as the next, that one can simply choose from. In fact, under the umbrella of Catholicism there are no denominations, as such. There are various ways to be a Catholic, and various Rites one might participate in, but not “denominations” in the same sense as Protestant denominations. It can happen that a “Roman Catholic” might become captivated by Eastern Christianity, and make a formal entry into an Eastern Catholic Church so that he is no longer a what most would call a “Roman Catholic”, but, say, a “Ukranian Catholic”. But to use those examples, Roman Catholic and Ukranian Catholic do not denote two separate denominations, the way Lutheran and Presbyterian do within the family of Protestant churches. The Roman Catholic who has gone over to the Ukranians (or vice versa) has remained in the same Church, under the same shepherd: the Pope.
As far as “denominations” that call themselves “Catholic” but which are not in communion with the Holy See (the Polish National Catholic Church, the Anglican Catholic Church, the Liberal Catholic Church, and so forth), a believing Catholic does not regard such bodies as possessing any authentic connection with the universal Church of Jesus Christ. So for faithful Catholics, such a “church” is no more a viable option than a Protestant denomination.
Now, many Catholics have and do leave their home parishes and go to others for one reason or another, but that’s just a matter of a Catholic finding a parish home that he feels comfortable in, or that presents the Catholic liturgy in a way that appeals to him more than perhaps his home parish does. But all Catholic parishes, of course, belong to one and the same Catholic Church, and the doctrine and sacraments do not change from parish to parish.