You're correct about arcanist and summoner both being pet-based classes. From what I've been able to gather, arcanist will be able to summon different types of carbuncle to fulfill different roles (tank carbuncle, melee carbuncle, etc.) and summoner will gain access to be able to summon avatars of the various primals.

Honestly, I'm not sure yet how second jobs fit in other than the fact that they've been confirmed in discussion with Yoshi-P that each class will get a second job at some point in the future. My best guess would be that going forward jobs will not only add abilities to the base class but also restrict certain abilities. This would give the dev team a lot more flexibility and allow greater differentiation between jobs stemming from the same class.

Take, for example, conjurer. Conjurer gains access to a number of spells ranging from cure and stoneskin to stone, water, and aero. Imagine equipping the white mage soul stone restricts access to higher-tier versions of offensive spells such as stonera, watera, and aerora while augmenting their skill list with additional healing and buffing spells.

Their second job then (geomancer?) might restrict higher-tier versions of the healing and defensive spells while offering access to more damage-dealing spells so that it can play as the water/stone/wind elemental offensive damage opposite black mage.

This would allow them to play up different strengths of base classes with different jobs. Archer could spec to bard for buff songs or ranger for more ranged-based damage specialization. Gladiator specs to paladin for tanking or dark knight for carnage. Thaumaturge to black mage for magic damage or red mage for magic debuffs. Arcanist theoretically specs to summoner for a wider range of summons, or scholar for sacrificing summons in order to gain something else (strategem based abilities?).