Strength of Magic

Regardless of where a Magus receives their training and magical education, all Magi recognize four distinct ranks of both power and sheer magical strength. Do not be decieved though, magical strength is not just about sheer power, but also about intellect and will, and careful clever application of magical knowledge. Apprentices have bested Masters that were relying on sheer magical power and strength instead of paying attention to the spells being used.
It is a truism among the Magi that "what ne person can do with magic, can be undone by another".
The differences in these ranks has to do with magical strength, breadth of knowledge, and power. In terms of sheer power, a Master is several orders of magnitude stronger and more knowledgeable than an Initiate. As one grows more powerful, and broadens their studies, the Magi are able to apply the strength they have to all of their techniques equally. The doctrine of "Knowledge is Power" holds true especially for the Magi, who accumulate considerable knowledge and thus considerable power as they advance.
Initiate
An initiate has just begun their magical training, or has recently finished his initial studies and is in the progress of deciding what else to study. Initiates are typically younger individuals and their paradigms are often very rigid and inflexible requiring substantial adherence to that paradigm. Initiates are often supervised a great deal in order to ensure their magical practice is sound and grasped.
Adept
As the Magus' knowledge grows, so too does his understanding of the interlocking and interconnected nature of all magical practice. From this understanding, the Adept is able to broaden his magical horizons, adopting another source and learning new techniques of magical application. The Adept is also initiated into the secrets of magical item creation.
Disciple
Disciples continue to build on what they have learned, expanding their grasp and understanding of magical principles. By the time a Magus has reached the rank of a Disciple, odds are they have taken on or will take on an apprentice of their own, and no longer have to deal with their Master looking over their shoulder and monitoring them constantly.
Master
Masters are Magi which have developed their powers across several different disciplines, and have attained a flexibility that is the envy of other Magi. In terms of sheer power, Masters command the most respect and even those that do not advertise their prowess are not to be taken lightly. With enough preparation a Master Magus can be the equal of almost any threat and can accomplish almost anything. Masters have reached the pinnacle of their power, and are unlikely to advance any further in magical understanding without succumbing to temptations which some might consider to be unnatural.

A hidden rank?
There are rumors of beings, of human beings that are called Archmages. These legendary beings are said to wield powers on the level of minor gods or Archangels, but no one has ever encountered an Archmage and been able to speak of it.
Magical Education & Training
It is nearly impossible for one to learn magic in a vacuum. While a person may be able to teach themselves the fundamentals from books, websites, and other resources, and perhaps even manage to perform the most basic of spells, their understanding will still be lacking without guidance and training from a more experienced Magus. The more novice a Magus is, the more closely they are monitored, with freedom to guide their own studies, conduct experiments, and test spells on their own coming as they demonstrate proficiency, understanding, and respect for the Art.