The online etymological dictionary gives the following:
c.1350, “of the doctrines of the ancient Church,” lit. “universally accepted,” from L.L. catholicus “universal, general,” from Gk. katholikos, from phrase kath’ holou, from kata “about” + gen. of holos “whole” (see safe (adj.)). Applied to the Church in Rome c.1554, after the Reformation.
O.E. crist, from L. Christus, from Gk. khristos “the anointed” (translation of Heb. mashiah, see messiah), from khriein “to rub, anoint,” title given to Jesus of Nazareth. The L. term drove out O.E. hæland “healer” as the preferred descriptive term for Jesus. A title, treated as a proper name in O.E., but not regularly capitalized until 17c. Pronunciation with long -i- is result of Ir. missionary work in England, 7c.-8c. The Ch- form, regular since c.1500, was rare before. Christmas is O.E. Cristes mæsse and retains original vowel sound; Father Christmas first attested in a carol attributed to Richard Smart, Rector of Plymtree (Devon) from 1435-77. Christmas tree first attested 1835 in Amer.Eng., from Ger. Weihnachtsbaum. Christmas cards first designed 1843, popular by 1860s.
O.E. cristnian “make Christian,” from W.Gmc., from L. christianus (see Christian). General meaning of “to name” is attested from c.1450.
O.E. cristen, from L. Christianus, from Gk. christianos, from Christos (see Christ). First used in Antioch, according to Acts xi.25-26. Christianity “the religion of Christ,” is from c.1303. Christian Science is from 1863.
"religious system revealed by Muhammad," 1818, from Arabic, lit. “submission” (to the will of God), from root of aslama “he resigned, he surrendered, he submitted,” causative conjunction of salima “he was safe,” and related to salam “peace.” Islamic is attested from 1791. Earlier Eng. names for the faith include Muhammadism (1614) and Ismaelism (1604), which in part is from Ishmaelite, a name formerly given (esp. by Jews) to Arabs, as descendants of Ishmael (q.v.), and in part from Arabic Ismailiy, name of the Shiite sect that after 765 C.E. followed the Imamship through descendants of Ismail (Arabic for Ishmael), eldest son of Jafar, the sixth Imam. The Ismailians were not numerous, but among them were the powerful Fatimid dynasty in Egypt and the Assassins, both of whom loomed large in European imagination.