No, the difference isn't experience. A 1st level Rogue and a 1st level Commoner are at the same place in life in terms of experience, both actual and numerical. There's actually been some interesting writing on this, but here's how it breaks down:
A PC has some sort of stat distribution. 32pt buy, 28pt buy, roll 6x 4d6 drop lowest from each batch, Elite Array, &c. All of those (yes, even Elite Array!) are drastically better than the stat distribution for any non-PC class. The average commoner is just that-average. They'll average out to 10 in every ability score, with an 11 in a score as an exceptional score as outright remarkable.
Characters with PC classes are already exceptional to a certain degree, but characters with PC stat distribution are the sort of individual you might see once in a generation. An ability score of ~18 is outright inhuman; 18 INT is a preternatural genius above the level of Einstein, 18 DEX is far and away the best gymnast and acrobat you'll ever know, &c.
Having PC class levels doesn't result in a character being exceptional, a character being exceptional results in them having PC class levels. That's how the game distinguishes people who perform beyond the human norm from the people who would be, all false arrogance aside, the contemporary equivalent of you or I as compared to Hercules or Merlin. And Hercules or Merlin, barring certain bits of their myths, are relatively tame as far as DnD adventurers go.
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Someone with class levels in "Ninja" would be a supernaturally talented spy and assassin. A historical ninja would be a Commoner with a couple extra proficiencies.