1) Catholic means universal or whole. With respect to the Christian Church, the early Christians used the term to refer to the whole undivided church. It is in that sense that all Christians today claim ownership of the term, including Protestants, although they often do not capitalize the term. The word dates from the patristic fathers and to the historic creeds and was used to set apart the mainstream body of orthodox Christian believers, from those adhering to mere sects or to heretical factions.
2) In countries which have been traditionally Protestant, Catholic will often be included in the official name of a particular parish church, school, hospice or other insititution belonging to the Roman Catholic Church in order to distinguish it from those of other denominations. For example, the name "St. Mark's Catholic Church," makes it clear that it is not an Episcopal or Lutheran Church. Using the word to differentiate between churches in this manner, arose when Protestantism appeared, making no claim on the word "Catholic". From long use in such countries, Catholic has become shorthand for the Roman Church used by Protestant and Roman Catholic alike. Orthodox churches still favor the terms "Western Church" or "Latin Church" in reference to the Roman Catholic Church.
3) Catholic in the sense of the physical institution of the One Holy Catholic and Apostolic Church is the usage intended by some denominations, such as the Eastern Orthodox Churches and the Anglican Churches — and of course, the Roman Catholic Church. The term "Apostolic" refers to the unbroken organisational and physical descent from the original twelve apostles down to the present. This descent of apostolic authority is emphasised by the laying on of hands when ordaining a priest. A statement of Use in this vein is made also by the Ancient Catholic Church, the Old Catholic Church, the Liberal Catholic Church and the Chinese Patriotic Catholic Association.
The Roman Catholic Church itself puts forth a particular sense of the term in the present context. In 1864 the Roman Catholic Church issued a letter asserting that "the Catholic Church alone is conspicuous and perfect in the unity of the whole world and of all nations, particularly in that unity whose beginning, root, and unfailing origin are that supreme authority and 'higher principality' (St. Irenaeus , Against heresies 3, 3) of blessed PETER, whom they call "prince of the Apostles", and of his successors in the Roman Chair. Their interpretation is that no Church is Catholic except the one which, founded on the one PETER, grows into one 'body compacted and fitly joined together' [Eph 4:16]..." (Denziger §1686).
The Roman Catholic interpretation is not the only possible reading of the passage from Ireneus. His specific language mentions "Peter and Paul" together in regards to the foundation of the Roman community of Christians, not giving primacy to Peter over Paul in the foundation or administration of Rome's community. Likewise, while Ireneus does list a short succession of Rome's Bishops, he also makes the effort to point out that St. Polycarp of Smyrna was in no way deficient in authority nor in doctrine in comparison to Rome, and actually brought correction to Rome when it fell into error.
4) Catholic may refer to any of a number of other groups which do not recognize the supremacy of the Bishop of Rome but who regard themselves as Catholic rather than Calvinistic or Puritan. Typical among these are "High Church" Anglicans, i.e., "Anglo-Catholics"). Often, this will be printed as "Catholic" but sometimes as "catholic".
5) The phrase "catholic epistles" is sometimes used to refer to the General Epistles of the Christian New Testament in the Bible because these epistles were not addressed to any particular city but to all in general. This use reflects its Greek derivation and is not necessarily intended to imply a relationship to a specific ecclesial community.
6) Capitalization is no sure guide to denominational affiliation. It may indicate formal affiliation with the Roman Catholic Church or it may not. Capitalization may indicate the holy and solemn nature of the spiritual body of believers. It emphasizes the desire for all Christians to be one. In that sense, it might seem ironic that a term designating the whole church should apply to one human organization only. However the Roman Catholic position would be that they constitute the original Catholic and universal Church, from which other groups broke away at various times in history.
The Roman Catholic Church, which makes insistent use of the term "Catholic" (e.g., in 1992 it published a "Catechism of the Catholic Church" or "CCC"), believes that the Church as a body is of divine institution, which influences their use of the term "Catholic". This profession can be observed in a number of dogmatic statements: in 1442 at the Council of Florence, the Bulla  "Cantata Domino" includes the phrase "The sacrosanct Roman Church, founded by the voice of our Lord and Savior..." (Denziger §703); in 1302 Boniface VIII in the Bulla "Unam Sanctam" refers to the Church as "that 'seamless tunic' of the Lord [Jn 19:23]" (Denziger §468); in 476, St. Simplicius  wrote an epistle containing the phrase "...the successors of him upon whom the Lord imposed the care of the whole sheepfold..." (Denziger §160). Roman Catholic theology thus incorporates the idea that the Roman Catholic Church is of divine institution, i.e. that Jesus imposed upon the organisational hierarchy the duty to care for the lambs/sheep (Jn 21:15-17), which is intended as a universal overture, as Jesus came to redeem man ("who for our salvation came down" in Nicene Creed).
The Roman Catholic Church does make some use of the term "catholic" as well, within theological tracts and dogmatic statements in which the universality of Roman Catholic theology is argued. This is more common toward the early period; the word is capitalized in English translations of dogmatic statements fairly early in Church history: e.g., St. Cornelius,  d. 253, wrote of the "most holy Catholic Church" (Denziger §44). An example of dogmatic use of minuscule-c "catholic" occurs in "The Creed of Epiphanius", longer form, which includes the phrase "one catholic and apostolic Church" (Denziger §14), thus asserting that the Church was intended to be universal, a usage to which is soon applied the greater dignity of the majuscule-C "Catholic". The Creed of Epiphanius (d. 403) is a slight expansion of the Nicene Creed, and some printings of it place the word "catholic" in majuscule form. But it is likely that the authoritative Denziger correctly renders the text; in the shorter form, Denziger §13, the word "Catholic" is placed in brackets, to infuse into the past writing the understanding that emerged, that the sense of unity and universality should be embodied in a more formal expression, in English rendered as a majuscule. Another dogmatic minuscule-c use occurs in the Denziger "Systematic Index of Dogmatic and Moral Matters," which lists "catholic" as a major category of dogmas surrounding the nature of the Church. In other dogmatic statements the Church uses the term "universal" in what appears to be an equivalent sense, though perhaps lacking the linguistic directness of implied universality which Roman Catholic theology proposes to have been bequeathed to the Roman Catholic Church by Jesus. Sometimes the "chair of unity" is referred to. A non-dogmatic — i.e. not propounded in strict definitional terms and without other criteria attaching — modern use of minuscule-c "catholic" occurs in the CCC §811 which quotes Second Vatican Council document Lumen Gentium §8, which in turn quotes a number of early creeds. Finally, see particular church for another example.
7. Many Protestant Christian churches — especially Evangelicals — avoid the term completely for what they believe is an important point of faith: that no mortal man can be head of the universal Body of Christ. This, they argue, denies the meaning of "catholic" as a "church for all people" or "a church for all nations", which they claim is just as valid an interpretation of "universal" as the idea that a single organisational body constitutes the Church. They believe that to suggest that the Pope could occupy the position of head of the church is heretical and a historical innovation dating only since the Great Schism. The Orthodox churches share some of the concerns about Roman Catholic claims, but disagree with protestants about the nature of the church as one body. Thus for some, to use the word "Catholic" at all is to appear to give credence to Papal claims.