—If you believe that the primary text in the tradition is the Decrees of Vatican II, and you're reasonably orthodox (i.e. could make a profession of faith and submission to the magisterium in good faith), then you're a "Neo-Catholic", and tend to have a lot of esteem for Pope St. John Paul II, often with little knowledge of the tradition prior to 1962, and sometimes with a habit of proof-texting from the 1990s Catechism of the Catholic Church.
—If you believe the primary text in the tradition is the Spirit of the Age, and you think that the Church is an unfolding reality which needs to become a prophetic expression of human potential leading the world forward into tomorrow, then you're a flipping heretic, aka "Progressive Catholic". Someone bring wood and oil.
—If you're a cultural Catholic who received the sacraments, were terribly catechized using McBrien or some other trash, and have more of a commitment to the politics and class priorities of your present millieu than to the Gospel, then you're a "Liberal Catholic". This takes two forms. The more common is the left-leaning liberal catholic, who thinks the Church should marry gays and ordain women and is just so mean for not being more accepting and up-to-date. The other variety is the right-leaning one, who likes the Church but is more interested in business and doesn't have much use for ethics beyond the general imperative to work hard and that sort of thing.
—If you attempt (with varying degrees of success) to be faithful to the tradition of the Church as a whole, and use Trent, Pius X, or some other authority or set of authorities from prior to 1958 as the lens by which you understand the tradition, then you're going to be a "Traditionalist Catholic". There are different flavors of "Trad".
- Some Trads are Glad, i.e. they're relatively at peace with V2 and try to ignore its defects in order to use it as an excuse to revive awareness of widely forgotten elements of the tradition.
- Some Trads are Mad, i.e. they're opposed to V2 either in its effects or in itself, and see it as the source in some way of our present woes, which include mass apostasy and the collapse of religious life, among other things.
- Some Trads are Rad, i.e. they're willing to oppose the governing authorities of the Church, which they perceive to be somehow infected with modernism or at least horrible imprudence.
- Finally, some Trads are Sad, i.e. they don't believe there's a pope at present, and are waiting for the restoration of the papacy.