the background is where/how the character grew up. the apprenticeship is their higher education.
i know where i grew up didn't teach me to be an educator, i had to study and take classes to learn that. my background is small town, my 'apprenticeship' is higher education...so to speak.
some backgrounds don't get apprenticeships. these are generally the backwoods places that don't offer higher learning, or groups that produce specific types of training already.
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It's sort of balanced by bonuses, with the game giving a rather high value to Bio-E. Your Feral mutant get's jack squat for skills, but a nice Bio-E bonus that should allow him to get that extra psionic ability, or natural weapon that the more skilled character can't afford with out dropping to a very short height or piling on the vestigials.