As an idea, theurgy can be applied very generally to a multitude of contexts and so long as they are reasonable, I do not think that it is inappropriate to do this. For example, I often use the term shamanism in reference to Native American religious practices, as is common among scholars, even though the term originated within a particular context, specifically, the indigenous practices of the native Siberians. On the other hand, like the term gnosis, theurgy has come to possesses many undesirable connotations that have become associated with it over time through what Schuon referred to as an abuse of language.
Many technical metaphysical terms have become inaccessible in western languages through both lack of use and the degradation of language caused by misappropriation. Recourse to etymology and contextualizing are two ways that can assist in the resuscitation of important terms such that we may clearly make use of and communicate their associated ideas. I think that separating gnosis from an association with the quasi-Christian movement of gnosticism and separating theurgy from an association with magick is a step toward resuscitating the proper use and understanding of these terms.
In its original context, theurgy, or "work of the gods" refers to the traditional rites of Hellenic worship. All religions contain a metaphysical doctrine which illuminates the deeper meaning of exoteric rites. Excellent examples of this are the writings of Psuedo-Dionysius in Christianity, Shankaracharya in Hinduism, and Ibn Arabi in Islam. The metaphysical doctrine that illuminates theurgy is Neoplatonism, or, as I prefer to acknowledge a continuity of the tradition, simply Platonism. The person who is most responsible for making this knowledge known was a philosopher named Iamblichus. In a period of time in which traditional Hellenic worship was at its greatest decline, he wrote a magnificent treatise On the Mysteries of the Egyptians, Chaldeans, and Assyrians that explicitly demonstrates the philosophical and metaphysical foundations of these practices and thereby serves as a justification for their continuance. What he did, in effect, was to make more visible to the public profound esoteric teachings which were traditionally reserved for a limited audience with the intent of reviving and preserving these traditions.
As far as the identification of theurgy with invocation is concerned, this is evident when theurgy is viewed comprehensively and the understanding of invocation is not limited to a particular technique. Tim Addey, a leading contemporary Platonist, describes theurgy in his work The Unfolding Wings, as follows,
"Theurgy, literally ‘work of the Gods’, ‘working with the gods’ or ‘divine work’, is an integral part of the Platonic Tradition; but because our knowledge of it has passed down through both the Christian era and the more recent so-called ‘rational’ one – both of which are largely opposed to the idea of worshiping pagan gods – it is an aspect of our tradition which is little understood or studied. This is greatly to be regretted because in truth it holds the key to the full understanding of philosophy, and brings the student of the deepest mysteries to the very portal of perfection … The elements of theurgic practice may be classified under the headings of prayer, hymns, sacrifice, ritual actions, invocations, and meditations and contemplations. We will look at these separately for the purpose of study but, of course, their power to draw the theurgic philosopher into a living relationship with the Gods depends upon their integration into a harmonious whole … Theurgy involves the invocation of higher powers: in truth all other elements of theurgy can be seen in terms of invocation.”
A greater understanding of theurgy may be obtained through an examination of Tim Addey’s book, Iamblichus’s work On the Mysteries and the magnificent study by Gregory Shaw called Theurgy and the Soul: The Neoplatonism of Iamblichus.