Theology, which is the spiritual preference of Western culture in general, means the study of God and/or religion. Theologians believe that believers may attain some sort of communion with or connection to God through a study of the Bible (His Word) as well as deeper research and discussion of the philosophies contained within the Bible. In other words, you can "know" God by learning everything about God.
On the other hand, the main tenet of Eastern mysticism is that God is a mystery, unable to be solved through human intelligence, no matter how much we study. Mystics commonly believe that there are other ways for us to commune with God, whether through certain rites and rituals, repetitive prayers, ceremonies, et cetera.
In summary, mystics offer "spiritual" ways to be close to God, while theologians offer intellectual ways.