It's based on your level and if you are playing as a job or a class.
Classes are the base forms of a job, and have access to all skills (though some are exclusive to just that class, like Cura is only Con/Whm)
It's 1-2 abilities per 10 levels. So 5 cross-abilities at level 50 Job, 10 as Class, I believe. Jobs are also restricted to 2 specific classes to pool actions from. For instance, Archer can use all abilities, but Bard, the advanced job, can only use Conjurer and Thaumaturge abilities (in addtion to Bard)