Not necessarily. The abilities are your own preference. Sometimes the abilities are mainly equipping abilities (i.e. Last ability learned for the Knight allows you to equip Swords for any job IF you set the ability). The stats are mainly in regards to Freelancer and Mime.

At the beginning of the game, Bartz is a Freelancer. As a Freelancer, his stats are 28 (Strength), 25 (Agility), 27 (Stamina), and 25 (Magic). If you choose to make him a Knight, his stats become 51 (Strength), 26 (Agility), 47 (Stamina), and 11 (Magic). Once you master the Knight Job for Bartz, his stats as a Freelancer become 51 (Strength), 26 (Agility), 47 (Stamina), and 25 (Magic). Notice how only the stats that are higher as a Knight remain higher as a Freelancer that has mastered Knight.

As you master more Jobs, the stats as a Freelancer and Mime will increase to the Mastered Jobs levels. However, they won't keep adding. If you master the Knight, and then master the Monk; your Strength will not be super-high, just whichever it was highest as (Knight OR Monk).