From birth a child will have a ‘natural class’ that they will possess in some strength for the rest of their life. This can be influenced (read: not 100%) during pregnancy by conversing to the Patron of a specific class group through the aid of an Oracle. The percentages of each class group (freelancers/warriors/thieves/mage classes/ranged) are roughly even in every region of the world but certain areas may have a small affinity for a particular class - nothing large enough to unbalance it, though.
Classes can be learnt over time, an ability not only vital to reduce infanticide but also to reserve complex classes to those who spend their life rigorously studying them. A child is not going to be a Necromancer or Chemist until they work their way up to those ranks through experience gain. That said, there will be Black Mages who will naturally be Necromancer-inclined and stronger at that class, just as there may be some that stay Black Mages for their entire life.
Skills are class-specific and generally provide a boost to the fighting abilities of that class. These can range from offensive/defensive abilities to flat stat modifiers. Skills cannot be ‘unequipped’ so once a skill has been learnt, that person possesses it for life. Some abilities rely on stats to determine their strength, so a Bard who later learns a Dragoon’s jump skill will not be able to use it as effectively as a naturally-born Dragoon.