In the first case, each is possessor; there are two lots of parents involved, and Nick and Jack need not be related. They may be school-mates, or friends, or cousins, but not brothers. Two apostrophes => two lots of parents.
In the second case, the possessor is a pair of brothers. One apostrophe => one lot of parents.
(It wasn't clear what you wanted explained, but I hope that does it . Whatever you wanted explained, it wasn't yourself: for a general explanation, you could ask 'Could someone explain?' or ' Could someone explain the difference TO me?')
Student or Learner