Magic" used by ordinary people is actually "para-magic." In essence, it is a technique which involves controlling energy.
Because ordinary people cannot use magic without the use of one of these, Dr. Odine developed Para-Magic. By studying a sorceress, he devised a way to manipulate energy to replicate spells. The would-be spell caster must "draw" a spell from an enemy or from a draw point. Using this drawn energy, the person can manipulate the energy in the battlefield to cast the spell.
"Para-" a prefix appearing in loanwords from Greek, most often attached to verbs and verbal derivatives with the meanings "at or to one side of, beside, side by side" (parabola; paragraph; parallel; paralysis), or "beyond, past, by" (paradox; paragogue). By extension "para-" came to designate objects or activities auxiliary to or derivative of that denoted by the base word, and hence abnormal or defective.
In Final Fantasy VIII the name is used to differentiate magic-use via junctioning systems (that anyone with access to the junctioning system can use) from natural magic (wielded only by sorceresses and monsters).
Magic or sorcery is an attempt to understand, experience and influence the world using rituals, symbols, actions, gestures and language that are believed to exploit supernatural forces.