Theurgy, and thaumaturgy are two types of categories of magick. These terms are used to show the difference between the results of what you will accomplish from certain types of magick, along with what you will be impacting. They are not meant to be limiting in any form of thought, or idea, or even show superiority in any sort of fashion. These are two terms that are very important for understanding the concepts of magick, and should be at least known and understood by the people who practice it.
Theurgy also known as high magick is a type of practice that is more focused on manifesting higher forms of understanding, and spiritual enlightenment. Theurgy comes to us from the Greek word θεουργία meaning God working. It usually pertains very highly to the gods, and the higher divine realms, because of this it is highly associated with religion, and usually calls upon the help of other spiritual beings. This type of magick is used in order to help the practitioner reach a state of apotheosis in their spiritual life, and experience. People that would do this type of magick would technically get the title of a theurgist. Theurgy gives the theurgist a higher connection to the divine, and other higher consciousness is in order to press their own growth through the act of experiencing, and interacting with these forces. The thought process of theurgy was greatly expanded on by the neoplatonist, and many other philosophical, and religious schools of thought. Theurgy is a lot more focus on higher purpose, evolution, and change of oneself, and is a much more spiritual type of magick. It is used to grow, and learn through the act of connecting with the divines, higher spiritual realms, other entities, and unseen forces. It is powerful magick for spiritual awakening, and unlocking the subconscious mind allowing the practitioner to grow, and expand spiritually, and mentally with their practices. There are a lot of magick’s that fit into this certain type of mold, such as most forms of ceremonial magick, divination, meditation, praying, invoking, and envoking, along with many others. This may also bring on more of an internal effect.
Thaumaturgy also known as low magick is a type of practice that is more focused on manifesting basic human desires. The word thaumaturgy comes to us from the greek words θαῦμα thaûma meaning “miracle” or “marvel”, and ἔργον érgon meaning “work”. Thaumaturgy is said to work off the capability of the practitioner in order to manifest their will, and desire upon the planes of existences. People that would do this type of magick would technically get the title of a thaumaturgist. Thaumaturgy is a much more practical type of magick, and it is used to call about your desires into the physical world, so that you can manifest them through your will. This magick is not exactly focused on spiritual growth, or awakening your consciousness, but much rather getting some form of physical, spiritual, or mental effect that can better your life, and some form of fashion. This type of magic would affect such things as love, money, health, luck, and career, among many other things one may desire. This may also bring on more of an external effect.