Ranks and jobs, although they may sound similar, are different things. Ranks are the level limit that you reach every 20 or so levels.
Jobs on the other hand, are what determine your stats, your playing style, almost everything. Here I'm going to help clarify the main differences between the two as well as touch on what OB, or Overbreeding, is.
Ranks are certain milestones you reach in your leveling. At different ranks, you're allowed to use higher leveled items. When I say higher leveled items, I am talking about weapons/armor only. The ranking system with usable items is odd in that it differs from the ranking system that equipment uses. I'll now list the rankings by level:
(I) Rank 1 = Levels 1-19
(II) Rank 2 = Levels 20-49
(III) Rank 3 = Levels 50-79
(IV) Rank 4 = Levels 80-99
(V) Rank 5 = Levels 100-120
(VI) Rank 6 = Levels 120+
Ranks for items are shown as the Roman numeral in the upper left hand corner of items. For those of you who don't know your Roman numerals, I've placed them next to the Rankings above as you have seen. The color code above is used in-game as well meaning items that are R3 will show up like this.
I mentioned jobs in the class section. Notice that some classes are able to split into different jobs upon getting their second job advancement. Second jobs are basically an extension of what your first job was; think of it as a promotion. You were able to do really well on your first job and you get to choose what you want to be as your promotion. In the case of pet classes, you only get one option. I'll kind of vaguely outline all the classes in order to let you get a feel for what each of the 2nd jobs really are. I'm actually going to skip the pet classes and I'll tell you why: There's only one choice for advancement so basically, whatever you're doing now as a pet class, you'll pretty much continue to do that.
Asura
Striders --> Assassin or Shadow Hunter
Assassins are the warriors that focus on stunning the opponent and finishing him/her off quickly before they have a chance to respond. Assassins dual wield either swords or dirks.
Shadow Hunters are crossbow-wielding killers that use different styles of attack. Each style affects the Hunter and helps him/her in various forms. With a variety of arrow skills, SHs are great at sniping things from afar and finishing them off before they get to them.
Dark Magician --> Chaos Magician or Warlock
Chaos Magicians are staff wielding fiends with an extremely wide arsenal of magical nuke spells to destroy opponents. With all these spells, who needs defense? For this reason, CMs tend to be more fragile than Warlocks.
Warlocks are a bit more versatile than their CM counterparts seeing as how Warlocks get an interesting OB boost in STR. For this reason, Warlocks can end up using Dirk and Shield instead of a 2H Staff. Warlocks are masters of destruction, but not in the same way as a CM: Warlocks tend to absolutely devastate the opponent with their debuffs. With all these debuffs in a Warlock's repertoire, Warlocks tend to lack diversity in the attack spell department, staying with the Dark Magician basics such as Fire Arrow and Lightning Bolt. This paragraph is also much longer than the CM paragraph because I'm biased. =D
Gaia
Fighter --> Champion or Archer
Champions are dual axe-wielding warriors that... well. Kill. Umm. That's kind of it. Sorry. =D
Archers focus on the strength of the bow to fight. Archers have a few traps and magic-infused arrows to stop the enemy in its tracks. As with all ranged classes, archers can be deadly from a distance.
Kahuna --> Battle Kahuna or Druid
Battle Kahunas are a bit more "reckless" in that they have a higher level of Recklessness buffs. These help the BH to be stronger in the attack spell department.
Druids are in-tune with nature and use their spells not so much to kill but rather to heal and support. Druids are more of a support cast when compared to Battle Hunas.
Deva
Holy Warrior --> Soldier or Knight
Soldiers can either dual-wield swords or use 2h Sword or Spear. Soldiers end up using their skills to weaken their opponent before going in for the finishing blow.
Knights are mobile tanks. Being high in HP and Pdef, they're ideal for taking damage for the group. These wall-like characters are intensely durable and can dish out some mean damage when necessary.
Cleric --> Priest or Bishop
In a nutshell:
Priest - Healing Cleric.
Bishop - Fighting Cleric.
Second job is only available after you reach Jlvl 40. It doesn't matter what level you are; as long as you have Jlvl 40, you meet the minimum requirements to get 2nd job. Are there Jlvls beyond 40? Why yes; jlvls go all the way up to 50 and cost an approximate 1 million JP. Now why would you do that to yourself? Simple: If you get to jlvl 50 before you get 2nd job, you get an extra stat bonus. I'll explain that in OB.
Overbreeding, or OB for short, is the process by which you get to Jlvl 50 before you get a second job. There are two types of overbreeding: OBing for yourself and OBing your pet. I'll go over the character type of OB first.
Overbreeding for your character will show no visible results other than the fact that you're going to have better overall stats. Depending on the job you're changing to, your stats will change too. When you get a Second Job, you get a stat boost based on what you're going to be doing in your next job. Here's an example:
Warlocks are a special breed of Dark Magicians who are more melee-oriented while Chaos Magicians are the second job form of Dark Magicians who focus more on casting spells. As you know, the STR and VIT stats are the best for warrior-like classes while INT and WIS are better for mage classes. The following are the OB stats for CMs and WLs respectively.
JLv 50 CM: 64 Str, 71 Vit, 65 Agi, 105 Int, 97 Wis, 65 Dex
JLv 50 WL: 67 Str, 76 Vit, 70 Agi, 93 Int, 91 Wis, 70 Dex
As you can see, Warlocks get a bigger STR and VIT increase than CMs do. Meanwhile, CMs get more INT and WIS than WLs do. As demonstrated, a lot of the stats you get when you OB are tailored to your class.
This doesn't mean that getting 2nd job at Jlvl 40 doesn't give you a boost; you get a boost, just not one as good as OB boosts.
Now, it's not uncommon to see people in their late-50s to early 60s (Not age wise. Now that's uncommon.) still in their 1st job state. They're probably OBing.
There is quite a bit of controversy over OB. Some people say it's not worth it simply because you only end up gaining a few stat points for a million JP when that 1,000,000 JP could be better spent elsewhere (such as 2nd job skills). Here is my personal opinion: OB. Because others in the same class as you may be ahead of you by some 1Mil JP but in the end, when both of you have all the same skills maxed, you'll be better off because you'll have the better stats.
Pet OB
Pets can OB also. It does the same thing: increases the stats. But when you OB a pet, you can see it being OB'd. Here's what I mean.
Here is a level 36 Pantera.
Now here is my level 56 Blue Pixie.
Notice the green number? That shows its progress in OB. Full OB is +10 for Evo 2 pets. I'll explain evolution in the pets section.
Here is what full OB looks like.

Tada. Full OB'd Orc.
Additionally, your pets gain an extra 2 JP per level when you start OBing. Pets normally evolve at level 50 but if you can get them to level 60 before evolving, you get the numbers next to the name as well as getting extra JP. This gives you extra 20 JP to use when your pet becomes evo2.
So if you had a pet that you didn't spend any JP on, without OB, the level 60 pet would have 60 JP to spend. With OB, the level 60 pet would have 70 JP to spend.
Again, I'm going to cover pets in the pet section.