Magic is the use of mana by magicians and magical creatures to cast spells. Not everyone can use magic. The ability to do so is determined by genetics, and those who are unlucky are in the bottom of New Salem society. In rare cases, this ability can be granted, such as when Nashwa gave Gina Evelyn the ability to use magic.
There are a few categories of magic: fire, ice, earth, etc. Magical creatures have affinities for certain types of magic. For example, fairies are strong with earth magic. Magicians can also specialize in these categories, much like how humans can specialize in their careers (e.g. carpentry, pharmaceutics, etc.).
There’s nothing preventing a magician specializing in ice magic from casting fire magic. As such, the categories of magic are just a classification. Any magician can cast a fireball if told how, much like how anyone can replace a flat tire if given instructions.
Within each category of magic is a set of well-known spells. When magicians first learn a spell, they start by chanting specific phrases, but those are only to assist in the process of manipulating mana. Over time, magicians can learn to use magic without chanting. Wands and staves also aren’t necessary for casting spells, but special components inside amplify their effects.
When a magician has used magic for a long time, they develop a deep understanding of how it works and are able to create their own spells. This knowledge is usually obtained by those who are the experts of their fields.