Both words have their origins in “knowledge” (-ology Gr. study of -; scientia Latin knowing) The modern “meaning” of science is the study of the physical, chemical, mathematical universe by certain methods of logic, called “the scientific method,” which submit to tests, such as repeatability). However, there are many “ways of knowing” (the study of which is called “epistemology”) besides scientific reasoning. Not incidentally, theology is not the study of a religion, but the study of God (Gr. theo-), by which is usually meant the study of the evidence for or against the existence of God, the forms in which God manifests himself (or herself or itself), and the history of God’s dealings with the universe, including Mankind. Theology is the study of the ways that Mankind has perceived, manifested, and related to God, in history and in changing cultural environments.
Now, theology is a science in that it gathers evidence, makes hypotheses and moves toward theories, as all history does (Joseph Campbell's study of myths can be called theology). But the physical scientific rules—repeatability, clinical studies, mathematical proofs, etc.--do not apply with the same strict rules. There is a convenient, if slightly equivocal, term—soft science—to cover such human knowledge inquiries as psychology, sociology, criminology, and, putatively, theology (perhaps a branch of that other soft science, history). The term “religion” is reserved for any one specific belief system, and should not be confused with theology.
There are many academics who do not think Theology is a proper subject for a modern university. 'The History of Theology' is a genuine subject, but, according to some, Theology is the circular discussion of the unprovable and unknowable.
Augustine of Hippo defined theology as, "reasoning or discussion concerning the Deity". Since there is no evidence for or against God, Theology cannot function under the application of the scientific method.
From Wikipedia's 'Theology' page...
Whether reasoned discussion about the divine is possible has long been a point of contention.