Base classes can use Cross-class abilities from more available classes than Advanced Jobs can. See more below.
Just to break that chart down a bit further. The "Name" is the Job title. "Abbreviation" is the game-designated term for the job. "Base Class" is the "origin" class, the one that levels concurrently with the job e.g. Wearing a Bard job stone will make you a Bard, but level Archer at the same time. "Subclasses" are a little trickier.
At 50, a class gets 10 cross-class abilities, from any equippable versions. A job, however, gets 5 job-specific abilities (from the job quests), and 5 cross-class abilities from the 2 listed subclasses ONLY. To unlock the job in the first place (to pick up the quest that gives the job stone), one of these subclasses must also be level 15, in addition to the base class being 30. I can't recall which one it is now in 2.0 (since those leaks were nerfed by SE), but it isn't random, or a choice - the quest will always have the same requirements.
For a concrete example, let's say you have a 30 GLA. You can have up to 6 cross-class skills, maybe you have a mix of LNC, PGL & MRD stuff for damage + survivability. BUT you want to become a PLD. The quest tells you that you have to have a 15 CNJ as well. You run off to Gridinia, and level CNJ to 15, then return to the quest, picking it up. You bust some heads, hand the quest in, and get a shiny new job stone. You slap it on, you're now a 30 PLD - grats! You now also have a shiny new job ability for PLD. BUT, you only have 3 cross-class ability slots to add to it, AND they can only be CNJ or MRD abilities, as they are your subclasses. You run around for a little while, and ding to 32. You take your job stone off. You're now a 32 GLA, and all those restrictions to cross-class abilities have lifted
The recommended strategy is to focus on a Base Class at first. According to Yoshi-P, you will not really need an Advanced Job until very specific scenarios at End Game. Edited, Aug 15th 2013 2:19pm by Gnu