Mages divide the types of magic into three broad families: elemental, living, and universal.
Elemental magic is the magic of the physical world. The most well-known types of elemental magic are air, fire, earth, and water, but lightning and ice mages are also common, as are types of magic which most people wouldn’t consider elements but which seem to fit better in the elemental category than any other, such as force. Elemental mages are the most common kind of mage by a long way, maybe more common than both of the other families put together.
Out of all the families, elemental mages are the best at directly affecting physical reality – they’re the artisans, engineers, and soldiers of the magical world, and it’s rare for them to come up against a physical problem they can’t solve. That said, their way of solving that problem is unlikely to be subtle. Elemental magic is usually very obvious and attracts a lot of attention. Keep getting straight flushes in a poker game and you’ll get some funny looks, but most people won’t think you’re using magic – they’ll think you’re cheating. Go flying down the high street and you’ll get quite a different reaction.
Elemental magic tends to be well-suited to combat. All elemental mages have at least some natural ability to hurt people and break things, even if it’s not what they specialise in. More importantly they can use shields, which give them a good natural defence against magic (and against most other things too). As a result, most battle-mages are elemental mages.
Living magic is the magic of living creatures and covers life and death, thought and emotion, and shapeshifting. While most mages can affect living creatures one way or another, living magic can alter them directly.
Living magic is completely unable to affect inanimate objects in any way, which means mages of the living family are much more limited than elemental mages in what they can do. An air mage is always surrounded by his chosen element – no matter where he goes, there’s air. (If there’s not, he probably has bigger problems to worry about.) A mind mage, on the other hand, can only affect creatures that have minds. If he’s on his own, he’s kind of stuck. Living mages also can’t directly protect themselves from physical harm in the way that elemental mages can.
That said, living mages have a few things going for them. When it comes down to it most important things in the modern world tend to involve dealing with other people one way or another, and that’s what living mages specialise in. Living magic also tends to be harder to detect than elemental magic, and living mages can blend in with ordinary people more easily than mages from the other families (although part of that is probably because living mages tend to be more social). Finally, while living magic can only affect living creatures, it’s very good at affecting living creatures and within their field living mages outshine everyone else by a long way.
Universal magic is the rarest, the strangest, and the most poorly-understood of the three families. It covers abstract concepts like divination, time, space, and chance.
More than any other family, universal mages of different types don’t have much in common with each other. A fire mage and a water mage and an ice mage might use different elements, but in a lot of ways they’re very similar – they can all shield, they can all gate, and they can all hit things with their magic until it breaks. On the other hand a time mage, a space mage, and a diviner have wildly different abilities. Some types of universal magic such as space can actually affect the physical world even better than elemental magic can (at least in specific areas) whereas other types like divination can’t affect the physical world at all.
If there’s one thing universal mages have in common it’s that they can do things no-one else can. A fire mage can put out a fire, but so can a water mage, or an air mage, or a guy with a fire extinguisher. But no-one except a diviner can look into the future, and no-one except a time mage can speed up or slow down the flow of time. Unfortunately this comes with a drawback: universal magic is the weirdest and most alien of the three families, and integrating it with a human mind isn’t easy. One of the reasons universal mages are rare is that a lot of universal novices never make it out of apprenticeship, whether for voluntary reasons (they give up their talents out of sheer exhaustion and go off to live a normal life) or for involuntary ones.