How does "theology" differ from "religion"?

In 2003, I asked Merriam-Webster the following question. Assistant Editor, Kory L. Stamper, replied as follows.

Q: How does theology differ from religion?

A: In general, “theology” refers to the theory and dogma shaping an overall belief system and metaphysical view of the universe, whereas “religion” refers to a body of sometimes ritualized religious practices as shaped by a particular theology. “Religion” is the earlier word, entering the written lexicon in the 13th century first to refer to the state of monasticism, then a member of a monastic community, then the community itself. It was not until the 14th century that “religion” came to be used of a particular system of worship and faith (as in the 14th century poem Cursor Mundi: In that siquar was in that tun Men of alkin religioun, or “at that time in that town [there] were men of all sorts of religion”).

“Theology” entered the written lexicon in the 14th century meaning “the study of God and of God’s relation to the world” and more broadly, “metaphysics.” The Oxford English Dictionary gives a fantastic explanation of the prehistory of the “metaphysics” sense of “theology” that has some bearing on the earlier senses of the word (with English transliterations of the Greek):

Note. Gr. theologia meant “an account of the gods, or of God (whether legendary or philosophical).” Varro, following the Stoics, distinguished three kinds of theologia, mythical, natural (rational), and civil, the last being the knowledge of the due rites and ceremonies of religion. This threefold division is referred to also by Tertullian and St. Augustine. In Christian Greek, the verb theologein was used = “to speak of as God, to attribute deity to,” whence theologia had the specific sense of “the ascription of a divine nature to Christ,” in contrast to oikonomia the doctrine of his incarnation and human nature. Another patristic Greek use, arising out of the primary sense, was “the account of God, or record of God’s ways, as given in the Bible,” whence the late Greek and medieval Latin use of theologia for the Scriptures themselves. In the 12th c. (1121-40) Abelard applied the term to a philosophical treatment of the doctrines of the Christian religion, which, though at first strongly condemned, became current, and, in this sense, “theologia” came to designate a department of academic study, the textbooks of which were the Bible and the Sentences (from the Fathers) of Peter Lombard. Hence the earliest English use. (The passage from Gower in sense 3 is derived ultimately from Aristotle’s division of the theoretic forms of philosophy into mathematike, physike, theologike the last being what we should call metaphysics, which included his doctrine of the divine nature.)

You can see that “theology,” then, was used in a much more “academic” plane than “religion” was. I believe this connotational distinction between the academic and the practical has carried through into more recent denotational senses of each word; “theology” is often used of a system of theoretical beliefs (senses 2a and b in the online dictionary) whereas “religion” refers to a set of practices and beliefs that theology (sense 2 in the online dictionary) influences. This has also affected later definitions: “religion” has gained the extended sense “a cause, principle, or system of beliefs held to with ardor and faith” and “theology” has gained the sense “a usually four-year course of specialized religious training in a Roman Catholic major seminary.”