Kerry is a Spellcaster; i.e. a Magecraft user who doesn't bother with the codes of conduct and honor of a Mage, using Magecraft as a mere tool. Otherwise known as a Heretic Mage. This is distinct to a Mage or Magus, who follows the whole Masquerade and honor and bloodline stuff, and this again is distinct to a Magician or Sorcerer. In the Nasuverse, there is Magecraft, the manipulation of the World internally, and then Magic, which is impossible manipulation that defies the rules of the World. At least nowadays; the Magecraft going back into the Age of Legend gets closer and closer to True Magic the further you go back.
There are Five True Magics. Denial of Nothingness, Operation of Parallel Realities, Heaven's Feel, some Fourth one that no-one knows about, and finally Magic Blue, Time Manipulation. Each is the domain of a ridiculously powerful Sorcerer bloodline and means a revolution in Magecraft. The ultimate goal of every Mage is to become a Sorcerer by reaching the Root, the source of all Magic - part of the reason for the Grail War. A Mage passes his heritage down to the next generation in the form of a Magic Crest - the accumulated knowledge of his life's work, which is then added to and expanded on by the successor of the family, and so on and so forth. It's tantamount to heresy to ignore your Magic Crest or disavow it, which is basically what Kerrytugu's done.
Similar to Magic (but on a much lower level) is the concept of a Reality Marble, the projection of innerly realized terrain onto reality. Basically, a microcosm which grants you a considerable advantage over your enemy, such as an unlimited field of legendary blades. Very rare and forbidden by the Mage's Association, the main Mage-controlling people. Mostly because none of their elite actually have one.
Kiritsugu's Magecraft is Time Alter, stemming from his family Magecraft of Innate Time Control going back about four generations. His father and grandfather attempted to give themselves immortality with their research, but he simply took the concept and worked out how to make a miniature field of Manipulated Time around him, similar to a tiny Reality Marble. Basic and not overly complicated, but ingenious and ridiculously effective, injuries aside. Put that down to the correction of the World.
In the Nasuverse, the World is a living entity. While its laws can be pushed around slightly with Magecraft and subverted with Magic, it always restores the status quo - that is, actively removes any anomalies that should not exist. Kiritsugu's pushing of the boundaries means that the World basically punches him in the face by restoring the flow of time immediately - so that's how his Magecraft works, at any rate.
The Origin Bullets are another thing entirely. Consider them his Mystic Code, the magical artifact used by Mages to perform the family Magecraft. The fact that they're bullets are incredibly heretical in themselves. His main advantage over every other Mage is that he actually uses Muggle weapons instead of Magecraft, and is really good at it to boot - memorising the heat signatures of Magic Circuits and sniping his targets, or using a night-vision scope to eliminate his targets instead of magical night-vision, or using cameras and claymore instead of familiars and Bounded Fields. Because most Mages are used to detecting prana (mana, but Nasuverse-style) instantly and disdain guns as inferior, he basically becomes this invisible ghost of bullet-shooting. Add that to his tactical mind and experience and he is quite the Mage-killing machine. Not too sure how it applies to unfamiliar magic systems, but he'll work things out.
Also, he isn't actually that great of a Mage, by virtue of all his Magecraft being used exclusively to kill. While he has an incredible theoretical grasp of almost every school of Magecraft in existence, he only limits himself to the most basic of techniques and Time Alter. However, he does know about voodoo-style enchantment (he's done some) and other stuff.
Noble Phantasms, by virtue of their legendary status, age, and belonging to Heroic Spirits, are far more powerful than any modern Magecraft - however, they're generally not on the level of Magic unless you count Ea.
Hope that clears things up.