Theurgy: means ‘divine-working’. The first recorded use of the term is found in the mid-second century neo-Platonist work, the Chaldean Oracles (Fragment 153 des Places (Paris, 1971): ‘For the theourgoí do not fall under the fate-governed herd’).
Thaumaturgy: means the capability of a magician or a saint to work magic or miracles. Isaac Bonewits defined thaumaturgy as “The use of magic for nonreligious purposes; the art and science of “wonder working;” using magic to actually change things in the physical world.” It is sometimes translated into English as wonderworking. A practitioner of thaumaturgy is a thaumaturge, thaumaturgist or miracle-worker.
While the goal of theurgy is unification with the divine and the goal of thaumaturgy is the accomplishment of practical goals, both share a great similarity in terms of the techniques used to accomplish their different goals.
All of the exercises to work with the senses and to focus the will remain the same. The primary differences exist in how the elemental techniques and Akashic/non-dual light are employed.
A thaumaturgist, also referred to as a magician, is primarily concerned with affairs in the physical and astral worlds. Manifestation of effects in these realms of existence largely center on elemental forces, vital energy from the power center in the guts, and astral energy from the solar plexus.
A theurgist is primarily concerned with the manifestation of Akasha and non-dual light to project his awareness into the mental realm, and beyond, where states of consciousness that exist beyond space and time reside.
Keep in mind the development of these phenomena exists in a continuum. A thaumaturgist will want to develop both Akasha and non-dual light to improve manifestation of the elemental, vital and astral energies. While a theurgist will still work with the elemental energies to strengthen their access to Akashic/non-dual light.
It is a matter of time spent on the different phenomena. A thaumaturgist spends much more time on the elements and a theurgist spends much more time on Akashic/non-dual light.