I'm going to speculate here that all characters will progress in terms of the "powers" they have at the same rate. They seem to be doing so in BAB, Saves, etc. and it would make as much sense to gain their special abilities at the same rate. One of the implications is that if a Fighter decides to pick up the Wizard Training feat then they would then be able to learn wizard "powers". So a 9th level fighter who took Wizard Training would then be able to select future at-will/per encounter/daily powers from the wizard list.
If those powers are organised in Talent Trees, then some of them may be prerequisites for others. So you might not be able to learn Fireball straight away, but once you'd taken two or three other spells from the Flame talen tree, that fighter would be able to use a fireball after they'd learnt a few other abilities, and that Fireball would differ from a Wizard's only because the person casting it would have a slightly lower magical attack bonus.
If those powers are organised in Talent Trees, then some of them may be prerequisites for others. So you might not be able to learn Fireball straight away, but once you'd taken two or three other spells from the Flame talen tree, that fighter would be able to use a fireball after they'd learnt a few other abilities, and that Fireball would differ from a Wizard's only because the person casting it would have a slightly lower magical attack bonus.