For simplicity I'll ignore the extra jobs introduced after Rouge/Ninja in this explaination of classes and jobs.
The class is what you choose by equipping a weapon. Swords for Gladiators, axes for marauders, Books for Arcanists, etc. These are your basic toolkits up to Lv30.
Jobs are unlocked at you get a class to lv30 (henceforth called the "base class"). This allows a specialisation within that class, along with a reasonable stat boost. You use a job ON TOP of the corresponding base class by equipping the corresponding soul crystal.
It's worth noting that as you level a job, the Exp earned goes to the base class, and the job's level IS the base class'. (you should see text like "Earned X Lancer exp points" while playing as a Dragoon)
The main example for this is the Arcanist, as that class has two jobs: Summoner and Scholar. As the player levels a Summoner, what they are in fact doing is leveling the base Arcanist. The upshot of this is if that same player has gotten to Summoner lv50 (thus the Arcanist beneath it is lv50), then goes and unlocks Scholar, the Scholar will start at lv50 as that's what the Arcanist is.
In short, you don't level the Job, you level the class. And as such gain any abilities from both as you level up as a job. So there's no gain from leveling the class separately, and it will in fact make your job harder without the stat boost the soul crystal provides, as well as the extra job skills/traits and unlocked specialised gear.