The word 'catholic' simply means 'universal', sometimes 'wide-ranging': "his tastes are catholic" means 'he likes many things'. Science is a catholic discipline. In archaic writing, it often has a final '-k' - catholick or catholik. (The word Catholic is derived from Greek (καθολικός, katholikos) 'general', 'universal' through the Latin catholicus as "general" or "universal".)
When written with an upper case first letter, Catholic is a religious term. It is usually applied to the members or beliefs of the Roman Catholic faith. The Eastern Orthodox Church also identifies itself as Catholic although unlike the Roman Catholic Church it is not in direct communication with the Pope. Catholic is a term to be handled with care, especially in discussing the Christian religion. "Catholic Church" should logically mean "Universal Church", and sometimes does, although there is no universally accepted form of Christianity; but many take the term to refer to Roman Catholicism. Many Protestant churches avoid using the word Catholic altogether. (Anglicans also describe their church (the (Protestant) Church of England) as 'Catholic', more so if they are High Church, or 'Anglo-Catholic': they claim to be the true descendant of the Apostolic Succession in England.) Contrariwise, Roman Catholics prefer not to use the qualifier 'Roman': they argue that theirs is the one true faith, and should not be localized. (It has been said "I'm a Catholic [= what is called here Roman Catholic], but I'm an Irish Catholic": Catholic is her denomination, and Irish is her nationality.) The Nicene Creed, still used by many denominations, includes the words "I [or We] believe in one holy catholic and apostolic Church"; the Apostle's Creed has "I believe in ... the holy Catholick Church". Both Creeds are in use in more than one church.
Among the meanings and notes given by OED (with AWE's underlining, and square bracketted additions) for Catholic are:
- "I. In non-ecclesiastical use ... 1. gen. Universal ... 3. In current use: a. Of universal human interest or use; touching the needs, interests, or sympathies of all men [or humans].
- II. In ecclesiastical use. 5. the Church universal, the whole body of Christians 6. a. As an epithet, applied to the Ancient Church, as it existed undivided, prior to the separation of East and West [the Great Schism, 1054], and of a church or churches standing in historical continuity therewith, and claiming to be identical with it in doctrine, discipline, orders, and sacraments. (a) After the separation, assumed by the Western or Latin Church, and so commonly applied historically. (b) After the Reformation in the 16th c[entury] claimed as its exclusive title by that part of the Western Church which remained under the Roman obedience (see 7); but (c) held by Anglicans not to be so limited, but to include the Church of England, as the proper continuation in England, alike of the Ancient and the Western Church. (Whatever the application, the implied sense is "the Church or Churches which now truly represent the ancient undivided Church of Christendom".) 7. As applied (since the Reformation) to the Church of Rome (Ecclesia apostolica catholica Romana) = ROMAN CATHOLIC ... (Opposed to Protestant, Reformed, Evangelical, Lutheran, Calvinistic, etc.)... ROMAN CATHOLIC is the designation known to English law; but 'Catholic' is that in ordinary use on the continent of Europe, especially in the Latin countries; hence historians frequently contrast 'Catholic' and 'Protestant', especially in reference to the continent; and, in familiar non-controversial use, 'Catholic' is often said instead of Roman Catholic.
Burchfield's Fowler adds a warning: "the history of the term [Catholic] is strewn with difficulties and complications, and these must be left for theologians to disentangle." If you are writing for a general audience - i.e. in almost all academic work - about the community of Christians headed by The Pope and want to specify that, use the term Roman Catholic. If you are writing exclusively for that community, it may be better to use the term Catholic.