Magician

A Magician (魔術師) is a person who is trained to use magic and is capable of transferring that knowledge. A 'normal' person can also use magic, as Tsukuyomi Komoe has demonstrated, though since they are ignorant of how magic works are incapable of teaching or transferring that knowledge, they are called Spellcasters. A normal person will suffer more severe consequences than a magician if they fail. At one point, Index states that people without mana cannot use magic, such as herself. However, this is a lie(though she believed it to be true), as mana exists in all forms of life, and it is revealed that Index can use magic, but is sealed off from directly using it outside of John's Pen.

Principles
Magic by itself roots from the simple fact that 'those without talent' wanted to be able to do the same things as 'those with talent', they gave birth to a ceremony and practice called magic, as stated previously the most important thing about magic is to prepare it properly, if the preparation itself is done correctly even a middle schooler with no magical talent might perform a spell ; the opposite stands true as if the preparations are not proper the magic not only will fail, but the backlash from it will fry the brain of the caster.

Magicians per definition prefer to operate in secrecy, even going to publicly deny the existence of "magic" if they are questioned about the subject and as such most people, such as Espers concentrated in Academy City are blissfully unaware of the existence of magic users, like Shirai Kuroko who mistook Sherry Cromwell as a Power User when the latter summoned a golem. Magicians are typically distinguished from Espers due to the former's use of items with occult properties and being able to yield more than one type of power at the time (such as magicians that can use more than one element, as the case of Oriana Thomson).

History of Western magic
Western magicians, though seemingly isolated to English magicians, carve their magic name onto their souls. Their magic name is normally the reason they took up magic, or the one dream which they would sacrifice their life for. An exception are Saints, who may carve it onto their chest/heart instead, as shown by William Orwell. Stiyl Magnus once said the real reason for having magic names is long forgotten, now it is only used in battle as a gesture to say 'it will now be a fight to the death'.

Western Magicians since the end of the 19th century, according to Tsuchimikado Motoharu, are beings that "whose wishes are not fulfilled, whose prayers to God went unanswered - people who have lost their way and turned towards this back door called Magic". According to him, most magicians are like children in the aspect they fight honorably and let emotion cloud their judgment - whereas other professionals such as soldiers will shoot without remorse; magicians are like "Children who hold knives. And also as Children who have been betrayed by the world, trembling and crying at the same time". As such, magicians have very little loyalty to organizations - they are willing to betray the group to which they are affiliated to if it somehow clashes with their own dreams/goals.

Other magicians (like the Etzali of the Aztecs) might not follow the Western rule of magic names, or became mages for the same reason.

Types
Western magicians dabble in a multitude of skills to do with magic, such as alchemy, astronomy, and summoning. Aureolus Izzard was called an "Alchemist" (錬金術師) because that was all he was good at out of the myriad of sub-sets of magic. In Index canon Alchemy in general is useless compared to other magic, and was renowned for being a trick for gullible nobles in the 16th century where they believed turning lead into gold was possible. Ars Magna was an exception in that it held exceptional power.

"Sorcerer" (魔導師) are magicians that have the purpose of spreading magical knowledge with the objective of raising the next generation of mages, according to Stiyl and Tsuchimikado these magicians are normally strong enough to handle the power of a grimoire and use it to teach the magical knowledge to their apprentices , Index also explained them with such characteristics.

"Magic God" (魔神) the highest possible position available to magicians where the magic of the user is almost considered divine and can overwrite the laws set by common sense. Other positions are possibly above that, such as "Saint" (聖人) or "The Person Superior to God" (神上), but they cannot be reached by 'normal' magicians and depends almost entirely on factors like talent or birth.