To get anything of benefit from the hierarchical representations of God's servants or ministers, we must first understand the foundational premise behind the formulation of a hierarchy in the first place, and also what an "angel" or minister of God is.
The Premise of Hierarchies in the Western Magickal Tradition
To the neo-platonists and their Christian successors, God was One. It's a simple concept. Orpheus says:
Pluto and Jupiter, and Phebus, are one;
But why do we speak twice? Gods one alone. (From Agrippa's Occult Philosophy, Book 3, chapter x)
The sh'ma of Judaism puts it this way:
"Hear o Israel, the Lord our God, the Lord is One."
The One God is beyond understanding, and is described in terms of what it is not due to our lack of ability to comprehend the awesome unity of God. "Ineffable," "Invisible," and "Infinite" are terms that do not tell us what God is, but what it is not. The mystic (by virtue of their calling to be a mystic) understands inherently that God is super-essential.
This super-essential Deity is constantly providing a stream of grace (or what we would likely call "energy" today) from itself into all that it created, in order that all of creation might participate with and know God intimately. This stream is called Providence by the Christian mystics, and is understood to be the mechanism by which Grace is delivered. When you see a mystic of neo-platonic christian heritage say that an event was "Providence," they mean that a person achieved "a closer and fuller understanding of God" (or Grace) through a series of events that might not have seemed to be Grace bearing in the moment.
Ok, so we have One super-essential God, sending Grace to creation by Providence. Since man is not capable of comprehending all of God at once in our standard mode, when God interacts with us directly, we interpret the aspect of God that we interact with as an entity, a messenger from God, or a representation of Deity, or a god in and of itself. The Goddess Venus, for instance, is that part of the One super-essential deity that represents the human understanding of "Love." In other cultures, this aspect of God is interpreted as Haniel, the archangel of the sephiroth Netzach.
To understand where this part of God "fits" in the whole process we interpret as Providence, we create models and hierarchies of correspondences so that we can present-progressively interact with that particular part of God as we perform our mundane activities. This touches on the practical purpose behind having a hierarchy in the first place.
The Purpose of Hierarchies
Having a model of Providence allows us to work towards obtaining unity with God. (Note: By unity I mean consciously working with God to accomplish God's purpose, not the idea that we can somehow consciously become GOD.) When one understands the aspects of God that are functioning at various points in Providence, one can begin to consciously integrate these processes into their daily activities. For instance, knowing that Cherubim means the fullness of divine knowledge, and that the function of this manifestation of God is to illuminate the soul of a man with the divine knowledge of the immanence of deity in all things, one would begin to work with the Cherubim when one is seeking to understand how a situation is supposed to integrate with God's plan.
This is the Great Work of the Western Mystery Tradition, to be in union with God in all things while in the flesh.
Having crudely put forth the foundational premise and purpose of hierarchies, we can look at what the various hierarchies are. For a better description, see The Celestial Hierarchies, by Pseudo-Dionysius the Areopogate, from which the above was distilled.
Some Traditional Hierarchies
The angelic orders of the "cabalists" are associated with the ten sephiroth. Following the lightning path, they are:
Kether - Haioth Hacadosch
Hochma - Ophanim
Prina - Aralim
Hesed - Hasmalim
Geburach - Seraphim
Tiphereth - Malachim
Nezah - Elohim
Hod - Ben Elohim
Iesod - Cherubim
Malchuth - Issim
That's straight from Agrippa, the original spelling from the English translation by "J.F." in 1651 intact. If you look in Book 3, Chapter x, you'll find much more additional information on these orders, such as the particular angel in charge, the planets associated with them, and the biblical personages and the angels that were assigned to them that correspond.
The terms Seraphim, Cherubim, Thrones, Dominions, Virtues, Powers, Principalities, Archangels, and Angels were used by Pseudo-Dionysius the Areopagate, a Christian mystic who was not a cabalist. Agrippa also uses these, and relates them to the sephiroth, but makes it clear in the text that they are not the names of the hierarchies used by the Hebrews.
Bill Heidrick has a couple of tables that present the names, correspondences to the sephiroth, and the descriptions and functions of these orders in his Magical Correspondences . Know going into it that Bill is the product of traditional Golden Dawn and Ordo Templi Orientis teachings. While his research and facts have been proven to be as accurate as possible, his interpretations are nevertheless influenced by the teaching he received.
To effectively utilize these hierarchies, the mystic or magician must first identify which order is appropriate to their need. Then one would research the names of some of the members of this order, and then contact the entity and request a personal representative from that order to work with for the duration of the operation.
Understanding the premise behind a hierarchy, the procedures of the magickal operations of the Western Mystery Tradition make a lot more sense. Abramelin's Sacred Magick is an excellent example, with the Holy Guardian Angel being a member of the Order of Powers assigned to you at birth, who "aids the human mind to break free of the forces that draw man to earthly thoughts." The Goetia can be better understood when it is recognized as a hierarchy of spirits that are closest to the manifest realm, a sub-hierarchy that doesn't quite extend beyond the realms of Earth, Water, and Air in the platonic model.
In conclusion, I would like to thank Richard Ryan for his Lamed towards presenting something of value and substance rather than simply critiquing someone else's presentation. Putting this into words has helped me to better understand some of the issues I've been struggling with behind the scenes lately regarding cabalism vs. neo-platonic christian interpretations of the Great Work.