White magic lv2 means you can get lv2 white magic when you set "white" as a command for a different job. When you are "maining" the job, you get all magic levels regardless of how many levels you have in the job.

Each line of spells in the menu corresponds to one level of magic. Black lv1 is fire ice thunder, black lv2 is uh... poison and some other trash i don't remember. black lv3 is fire 2 ice 2 thunder 2.

If you know Fire 2, but only have black lv2 learned, that character can not get access to fire 2 if you set !Black as a sub ability when you are a knight or a white mage.

I usually make galuf a monk in the beginning, then change to a mage when he learns barehanded.