Global cooldown is 2.5s for all jobs. Mages get cast time as well that for some spells is longer than that. Spellspeed/skillspeed reduces the global cooldown and cast times.

There are also various cooldowns available to reduce cast times(swiftcast(thm/blm - shared with all casters), ley lines(blm), lightspeed(astrologians), presence of mind(white mage), a rng based spell speed up based on pet criting(scholar/summoner/archanist)).