Magic Attack and Magic Attack Bonus are different in that:
Magic Attack is a statistic gained from a job ability.
Magic Attack boosts all Blue Mage elemental magic spells that deal damage, and only BLU-specific spells (i.e. Blastbomb, Radiant Breath, 1000 Needles)
Magic Attack Bonus is a Job Trait, a passive ability gained from leveling certain jobs.
Magic Attack Bonus works with elemental spells cast by jobs other than BLU which are based upon modifiers built around attributes, elemental weapon skills (e.g. Red Lotus Blade, and Corsair's Quick Draw.