Do you prefer it when games have class systems or job systems?

As for what the distinction is, here is how I would define it.

In a job system, in contrast to a class system:
* Your advancement in a job, assuming such mechanic is present, is separate from your experience level. In other words, advancing in your job is separate from growing in power overall.
* You can easily switch jobs. Doing so will only have minor (if any) short-term effects on your stats. In particular, doing so will not send you back to level 1, and this can be done at will rather than having to be done at level up time. In particular, such games allow and sometimes even encourage frequent job switching (like Final Fantasy 3 expecting you to change your entire party to a specific job for one specific boss fight).
* Changing back to a previous job is allowed, and allows you to continue improving that job right from where you left off.
* In job systems, it is typically common to allow the player to choose a sub-job or ability from another job; the sub-job won't be advanced, but any abilities from it can be used. (In contrast, class systems that allow class changing (which not all of them do) may allow you to keep all abilities of a certain type (like spells) rather than having you choose what you want to carry over.)

So, which do you prefer?

(I prefer job systems, as they lead to your set-up more fluid, as you're not locked into the same party setup the entire game.)

I guess it depends on how much I'm getting paid for the job and what I can learn in the class.

Jobs are just the Final Fantasy term for classes ;)

In FF1, at least on the NES, the manual used the term "class", and I think the game may have as well.

Neither, Fates!

I don't think I've ever played an RPG with a "job system" outside of the few Final Fantasy games I played (6, 7 and 8).

None of those FF games have job systems. 3, 5, and Tactics have them. 1 and the International Zodiac Job System version of 12 have class systems (yes, FF12IZJS calls it a job system, but it behaves like a class system, since there's no changing between classes). Also, Dragon Quest 6 and 7 have job systems (while 3 and 9 have class systems).

Tangledeep and Fell Seal: Arbiter's Mark have job systems, and are both available on GOG.

At this point you are just hung up on semantics. In FF13 they call it roles. It's the same as classes, job, callings, profession or whatever else you could call it. They just try to be flavourful with their naming.
And if you really can't see that they are the same thing functionally in those games, then you should take a step back, go out and learn a profession, try to find a different calling, maybe reach a higher class, but whatever you do, at least abandon your role as the forum pedant.

Pain au chocolat ou chocolatine ?

Can I say neither? Free character development, just advance whatever skills you want. Even better if all of them, eventually, if you control a single character.

If I must pick though, according to your definitions, classes. If "jobs" can be frequently changed then, as you also say, it may be expected that you do so, and that'd be too taxing, to always look for the right one for the situation and likely have to change playstyle along with it. Plus, hard to make sense story-wise. (I know, I know, for you story just detracts from gameplay. Not how I see it in the least.)

There is a functional difference between what I call "classes" and what I call "jobs". A class is something that the character has long-term, possibly permanent, and is either unchangeable or comes with significant cost to change. A job, however, is something that you can change pretty much at will, without serious consequence, and therefore something that you might easily change many times during the course of the game.

So, there is a difference, in terms of whether your characters' abilities are rigid (classes) or fluid (jobs).

I'm currently playing Dragon Quest IX, which has a "jobs" system. It gives the ability to change party composition as desired. Some skills can be transferred over to the new class, to add versatility or reinforce a specialization. Unfortunately, it takes a ton of grinding to reap its benefits.

The only RPGs with jobs that I've played are FFT and FF5, and while I love them, I wish there's a way to switch and try different jobs at roughly similar level without excessive grinding from Job lvl. 1 all over again. Like, give us generous respec points, or a spillover Job Points for adjacent classes (e.g. for every 10 JP you get as a Knight, you get 2 JP for every other physical-based jobs (Monk, Samurai, Ninja, Dragoon, etc.)).

I consider this to be more of a class system. Specifically:
* Class level is not separate from character level; they don't grow independently.
* When you change to a new class, you go back to level 1, with level 1 stats (though you at least get to keep stat boosts from skills). Hence, there is a real cost to changing to a new class.
* You don't get to choose what you carry over; all learned skills carry over, but no spells do. (This is actually the reverse of how games like Wizardry 1-5 and Dragon Quest 3 handle it, where spells are the *only* abilities you keep.)

On the other hand:
* If you change back to an old class, you do get your level and stats back, and can continue right where you left off. (This is not the case in, say, Wizardry 1-5 or Dragon Quest 3.)

Incidentally, for other Dragon Quest games with class/job systems (excluding 10, which really should have been called something else (Dragon Quest Online?) due to being a MMO):
* DQ3 is a classical example of a class system. Change class, you're back to level 1, you lose half your stats, but you keep your spells (but nothing else). Changing back to a previous class will send you back to level 1 minus half your stats, so you have to start over (instead of continuing where you left off).
* DQ6 and DQ7 are job systems; you advance in your current job by fighting a certain number of nontrivial battles, and that advancement is separate from character level. Job changes will not force you back to level 1 or cause significant stat loss (other than losing one job's stat modifiers but gaining another's), and you can change back, continuing right where you left off.
* The rest of the series doesn't have this sort of system; each character has fixed roles and abilities, though later games (starting with DQ8) have a skill point system which gives you limited choices within the character's class (though note DQ9 combines it with a class system that allows class changes, as mentioned above).

(Note: All mentions of Wizardry 1-5 can be assumed to not include Wizardry 4, as that game is not like the others, and it does not make sense to talk about Wizardry 4 in this context.)

FF5 does do something nice; a character is immediately effective in the new job after changing. Change into a white mage, and the character can cast every white magic spell you've acquired, even without leveling the job.

The only reasons you may need to get ABP in FF5 are:
* To use the job's abilities in a different job.
* To use abilities the job can learn but doesn't have automatically (the most important being the Knight's two-handed, the Chemist's Mix (which should have been the job command instead of Drink), and the final abilities of certain jobs (Dualcast and Rapid Fire come to mind here).
* To improve the character's stats in the Freelancer and Mime jobs, and transfer innate abilities. (This is something you should only be concerned about late game, and it is not at all necessary to do this.)

Also, I note that FFT has vicarious JP; when a character gets JP, other characters get a small amount of JP in the same job. (Interestingly enough, Fell Seal: Arbiter's Mark copied this mechanic, as it has vicarious AP.)

(By the way, from what I can tell, if you loved FFT you should check out Fell Seal: Arbiter's Mark; it is very clearly FFT inspired.)