There is one Church. There are hundreds of factions (after all, any organization of sufficient size will have political infighting). Then there are many people who claim to be Catholic but are really heretics in sheep's clothing.
Sedevacantists are people who deny the validity of the current Pope as well as the Second Vatican Council. That is more-or-less like denying Nicea. You can't do it and manage to escape the title "heretic."
Conclavists are (most often) sedevacatists who have gone so far as to say, "since VAII was heresy, the bishops who supported it are heretics. Heretics are incapable of properly electing a pope. Therefore, there is no pope and the See is vacant."
I do think that it is a good idea to expand a bit on your title, even though that is not your full question. There are quite a few different liturgical and spiritual groups inside the Catholic Church. Most commonly, you will find Byzantine and other Eastern groups who closely resemble the Orthodox in both practice and theological expressions, but there are other, smaller sub-organizations in the Church (such as the Ambrosian Rite (which is largely liturgical) and the Anglican Ordinariate (which is only a few years old and closely resembles the ways of the Anglican Church)). Depending how you subdivide it, you could even argue that every major order (or even every abbey) can be considered a subset with its own customs, beliefs, and traditions. For that matter, even within a diocese, you will find different parishes behave different ways.
And now, a joke:
Why is it easier to convert an atheist than a conclavist?
At least an atheist believes that there's a Pope.