There is a bit of both, depending on the kind of magic you're dealing with.

Magic is a rare talent in this era of the world. Those who wield it are born into it, experiencing a huge surge of power at some point in their childhood/teenage years. Now, in this world, magic is categorised by [b]source[/b]. A variety of factors tie a mage to a particular source, and as they grow as practitioners of magic, they become more attuned to the source of their power and are unable to draw from any other source.

That probably isn't very enlightening, but feel free to keep asking me questions.

Now, your second question. It depends on a variety of factors. Like artists and writers, mages have a particular 'voice' or style, tied in with their own personality. A boisterous personality will evoke a more visual and flamboyant style of magic, whereas a timid personality will likely be less confronting and perhaps more subtle. [b]EXAMPLE[/B]: now, take Mayven (a random name, purely for this example). Mayven is a stormsinger, a practitioner of elemental magic. Mayven is silent, cold and brooding, and his style of magic reflects this, finding thunder, lightning and rain too vexatious to call upon and control, he instead prefers evoking the power of a blizzard. He doesn't appreciate large, destructive displays of power, so he's all about plummeting temperatures, harsh gusts of cold wind and creating small snowstorms.

Secondly, the concept of your 'power cap'. Magic is exhaustive to the human body. It requires concentration, focus and a great deal of endurance. Some mages have lower power caps, and are therefore unable to perform greater feats of magic (or do, at great consequence to their mental, emotional and/or physical health). As a result, they would focus on smaller and less flashy displays. [b]EXAMPLE[/B]: Mayven has a very high power cap, something common for stormsingers and practitioners of elemental magic. However he recognises the consequences of breaching his cap. He has seen other stormsingers driven insane by the stormsong, and some others consumed by the storm and killed by powers they couldn't control. When Mayven was younger and curious about the extent of his power, he called upon a great blizzard, of which he was soon unable to control and as a result lost several fingers to frostbite.

Thirdly, the source of your power. Not only does your source of power influence what kind of magic you're dealing with, but also your power cap. There are several main sources including leyline energy (arcane magic), daemons (black magic) and nature (elemental/wild magic). [b]EXAMPLE[/B]: Mayven is a stormsinger, who draws his power from the skies, and as such he deals with some pretty badass magic. His brother Yrailan, however, is an abjurer who utilises subtler notes of arcane magic to create protections and wards.

And yeah. Another factor is, of course, what you're trying to achieve and the spells you're performing.

Not sure if I've helped or probably confused you more.