The most basic thing for an Exorcist, the term refers to the skill(s) the Exorcist uses to fight demons. Some choose to specialize in just one form of combat, but having multiple is common as well. Some powerful exorcists even practice all 5 types.
These exorcist's summon and tame demons to fight for them. These demons are called "familiars". A magic circle is needed to summon them, and if the circle is broken or torn (if its on paper) the demon disappears. To summon the familiar, the exorcist must recite certain words and drop their blood onto the circle. The magic circle can be on the ground or on paper, or even tattooed onto a person's skin. Also, familiar's will sometimes turn on their masters if they seem to lack confidence. Tamers are rare due to the natural talent and magical skill it takes to summon and control demons.
A knight is an exorcist that fights demons using swords. Most knights use powerful demon swords to do so. Knights seem to be one of the stronger skills, but it really depends on the power of the sword as well.
Exorcists that use guns to battle demons. They seem to be the most modern, especially when compared to Knights and Aria. Any range of guns can be used, from simple hand-guns to machine guns.
Most demons have a weak point called "The Fatal Verse", these are certain phrases or lines from Holy Scriptures that cause the death of said demon. Aria figure out the Fatal Verse and recite it to battle demons. They are fairly vunerable when doing this however, so they rarely fight alone.
An exorcist that can heal wounds and and injuries inflicted by demons.