Before we begin, I'll acquaint you with the difference between referring to yourself as Catholic and referring to yourself as Christian as I know some -- or even, most -- of you may not be familiar with such. Like most of my articles, I will use diction to my advantage.
1. a set of beliefs concerning the cause, nature, and purpose of the universe, esp. when considered as the creation of a superhuman agency or agencies, usually involving devotional and ritual observances, and often containing a moral code governing the conduct of human affairs.
2. a specific fundamental set of beliefs and practices generally agreed upon by a number of persons or sects: the Christian religion; the Buddhist religion.
3. the body of persons adhering to a particular set of beliefs and practices: a world council of religions.
4. the life or state of a monk, nun, etc.: to enter religion.
5. the practice of religious beliefs; ritual observance of faith.
6. something one believes in and follows devotedly; a point or matter of ethics or conscience: to make a religion of fighting prejudice.
7. religions, Archaic. religious rites.
8. Archaic. strict faithfulness; devotion: a religion to one's vow.
9. get religion, Informal.
a. to acquire a deep conviction of the validity of religious beliefs and practices.
b. to resolve to mend one's errant ways: The company got religion and stopped making dangerous products.
1. a religious group, usually including many local churches, often larger than a sect: the Lutheran denomination.
2. one of the grades or degrees in a series of designations of quantity, value, measure, weight, etc.: He paid $500 in bills of small denomination.
3. a name or designation, esp. one for a class of things.
4. a class or kind of persons or things distinguished by a specific name.
5. the act of naming or designating a person or thing.
1. of or pertaining to a Catholic church, esp. the Roman Catholic Church.
a. (among Roman Catholics) claiming to possess exclusively the notes or characteristics of the one, only, true, and universal church having unity, visibility, indefectibility, apostolic succession, universality, and sanctity: used in this sense, with these qualifications, only by the Church of Rome, as applicable only to itself and its adherents and to their faith and organization; often qualified, especially by those not acknowledging these claims, by prefixing the word Roman.
b. (among Anglo-Catholics) noting or pertaining to the conception of the church as the body representing the ancient undivided Christian witness, comprising all the orthodox churches that have kept the apostolic succession of bishops, and including the Anglican Church, the Roman Catholic Church, the Eastern Orthodox Church, Church of Sweden, the Old Catholic Church (in the Netherlands and elsewhere), etc.
3. pertaining to the Western Church.
4. a member of a Catholic church, esp. of the Roman Catholic Church.
In summary, a denomination is a sect or "branch" of a Religion. You can imagine that a Religion is a tree trunk and each branch -- the denominations -- protrude outward. Sunni and Shi'a are examples of denominations in Islam, while Catholic, Baptist, Lutheran, Methodist, Orthodox, et cetera are examples of Christian denominations.
In Christianity, the denominations are separated into two major categories; Catholic and Protestant. This is the divisive point of the tree's trunk, where it splits in two. A fair representation of the relationship between the two can be found here.
The divisive point began in 1517 Anno Domini as a direct (or indirect, if you want to argue certain factors) result of a Catholic monk by the name of Martin Luther (not Martin Luther King Jr.) Before this time, much of Europe was in absolute control by the Roman Catholic Church.
In protest to the sale of indulgences (scrolls one could purchase from the Church which, supposedly, granted them instant access to salvation.), Martin Luther wrote the 95 Thesis (a thesis with 95 criticisms of the Catholic Church) and nailed it to the door the cathedral he serviced.
This sparked the Protestant Reformation and Martin Luther was put on trial for heresy. He was to plead his case and renounce the content of his work or face excommunication (being banned from the Church.) However, his refusal marked him as a refugee; his response: "Unless I shall be convinced by the testimonies of the Scriptures or by clear reason ... I neither can nor will make any retraction, since it is neither safe nor honourable to act against conscience."
During this time, many attempts were made to try to reform the Catholic Church, but it ended in a lot of bloodshed; this period is known as the Peasant's War. As this was all going on, Martin Luther translated the Holy Bible of the time into the language of the common man, German and omitted the biblical apocrypha (controversial books -- or chapters -- in the Bible that, for one reason or another, were deuterocanonical; also referred to as the Antilgomena by Protestant faiths.) This sparked great dishevel among the two factions which dragged on in the years following and resulted in the Catholic Counter Reformation.
That's a basic summary of events, anyway. For further reading, you can start off with the Wikipedia article on the Protestant Reformation (and perhaps on Martin Luther, himself, if you're interested), but I'd suggest you garner other sources for your repertoire. That will conclude the history lesson for now as it was only a staple to acquaint those unfamiliar with such matters with the underlying principles of the Catholic/Protestant Debate.
We'll move onto the actual debate now.