Does rolling Critical do anything different that a normal hit? Lose a shield token + a damage card or damage card face up?
It's outlined in the main rulebook in the box (and indeed I believe the rules are online).
Normally, a critical hit does a damage card like a normal hit, but it's face-up (and follow whatever special effect is listed on the card). The text on face-down cards is ignored, and you don't know what they are. There are a few pilots, crew and upgrades which let you manipulate this, though, flipping cards face-down (or cards on opponents face-up).
There are a few pilots and weapons which do other things with critical hits, but it's easier to look at them pilot by pilot rather than try to list them all. As an example, Kath Scarlett (an Imperial Firespray Pilot) causes you to gain a stress token whenever you evade a critical result from her attacks.
It the 'learn to play' quick-start rules, then no, there's no particular difference between hits and critical hits.
Criticals don't do anything special to shields - a shield token absorbs one uncanceled [hit] or [critical hit] result, and doesn't care which.
This is why shields are deceptively powerful, especially on agile targets like a TIE/
fo.
Because you always cancel [hits] before [crits], if you have lots of red dice and lots of green dice, then the odds increase that if any damage does squeak through, it'll be a [crit], which means that agile targets like TIE fighters and TIE interceptors take [crit] results a disproportionate amount of the time. Which hurts, because - lacking shields - they always suffer the bad stuff associated with the critical hit.
Equally, an X-wing has Target Lock as well as focus whilst a generic TIE fighter doesn't (I realise that TIE/fos do, but stay with me here). Whilst both give you the same average increase in damage output, a focus token converts [focus] results to [hit] results, whilst a target lock rerolls both [focus] and [blank] - both result in an average of 75% of the dice you roll coming up damage, but target lock slightly increases the odds of getting [crit] results, whilst focus doesn't.
These two factors, together with shields ignoring criticals, are the reason criticals tend to bug Imperial players in TIE fighters and TIE interceptors far more than Rebel players in X-wings and B-wings.
One of the defining differences between the Rebels and the Empire is that the durability of Rebel ships tends to come from shields, higher damage capacity, and the ability to fix damage after it's suffered, whilst the Imperials generally have more green dice and a much greater ability to manipulate green dice rolls and/or generate tokens which do the same.