Magic is passed on the X chromosome. Due to mystical and chemical interactions surrounding have two X chromosomes, all females with at least one active magic gene will have their magic rooted in either light or dark. This is immutable and causes a magical female to be either a light fairy or a dark witch. Since males have a single X, their magic is neither light nor dark, and all are simply wizards.
Fairies are women with light magic. Their powers are activated by transformation into their winged forms, which allow them to fly and exercise their abilities to their fullest extent. After the first transformation, a fairy may use magic in her untransformed state, though her power will only be a fraction of what it is when she is transformed. Because fairies use wings to fly, the fairy gene enforces a light and aerodynamic body type.
Fairies increase their power by earning transformations through quests both internal and external - to earn Charmix, one must face their fears; to earn Enchantix, one must sacrifice oneself for another of their home realm. Once a fairy has earned a transformation, she immediately is able to use its full strength without a learning curve. A fairy is also only able to use special powers associated with higher transformations when in that transformation - for example, an Enchantix fairy cannot use her fairy dust in her initial transformation state.
Witches are women with dark magic. Their powers come naturally without transformation, though one can activate a transformation glamour for aesthetic and/or intimidation factor. Witches can fly without wings and without transformation, so they come in a variety of body types.
Witches increase their power by studying and practice. They do not gain power quickly, but a dedicated witch can amass incredible strength over her lifetime and use it on whim. Witches do not have natural power ups - note that canon abilities such as Gloomix and Disenchantix were bestowed upon the Trix by their villain sponsors.
Wizards are men with magic. They do not transform and do not have specific power sets like fairies and witches do as a result of the neutrality of their magic. They may augment their powers with magical items, such staffs or other useful objects and crafts.
A founding principle of the Magical Dimensions is balance (though given the way that present society has gone with favoring the light, it is certainly difficult to believe). In order to maintain the balance, at any one time there exists one fairy and one witch with domain over a specific area. For example, there is both a fairy and witch of the Sun, Moon, and Stars. Whenever one dies, another is born to replace her. This fairy and witch do not necessarily have any connection to each other whatsoever, though siblings have been known to be a pair - for example, Flora and Miele are the Witch and Fairy of Nature.