The main difference between Summoners and Tamers was the creatures they were capable of beckoning to them. Tamers could only subdue creatures within Aigas while Summoners could only make contracts with creatures trapped within Stagnant Space or the Abyss, as the Cavern called it.
Summoners had to traverse to the Abyss with their consciousnesses and attract beasts that would be interested in joining hands with them; which meant their Class was rather costly. Even when they succeeded, Summoners needed huge energy reserves to summon the contracted beasts; these creatures couldn't be stowed somewhere in Aigas, after all. They had to return to the Abyss after the terms of their use or cooperation.