Espers

Espers (or Eidelons) are not gods, but demi-gods at best. They are not immortal, but are powerful creatures that can be summoned through a number of means. Whatever form a summoning takes, the Espers are never actually removed from their home in the Feymarch. Most of the Espers who were once forced into Magicite and were 'killed' within the World of Magi (FF6) still exist within others, and so they were reformed in the Feymarch with the creation of the World of Ruin, although their Magicite forms still remain.

Standard Summoning

When someone calls/summons an Esper, they are only really calling forth a mote of their true power. A part of the Esper is projected into the world from the Feymarch, and after their task is fulfilled, that part returns to the Esper. They have no recollection of the summoning in most cases - though there are always rare exceptions. In the case of casting an Esper from a Jewel or Magicite, it simply serves as the 'focus' for their power.

Dark Summons

Those with a dark heart may have the ability to summon a tainted variant of an Esper. These are not separate beings, but manifestations of the darker part of each Esper that correspond to those within the summoner. For most intents and purposes, these summons work the same as Standard Summons, and have no effect on the Esper themselves within the Feymarch.

Guardian Forces

There are rare times that Espers travel outside of their own world, and that is to form a contract to become someone's Guardian Force. Beyond this personal interaction with their summoner/caller, there is no real difference between the use of one of these Guardian Forces and a traditional Summoning. However, the 'part' that the Espers give up to these people in Junctioning with them does grant a certain sense of 'relationship' between the two.

Aeons

Aeons are dreams of Espers from another world. Though Zanarkand lies in ruins in this world, the Aeons continue to dream up their version of the ancient city. With those dreams living on, the ability to summon forth those memories remains. When Spira became fused into the World of Ruin, some locations became part of vastly different lands. Summoners seeking to gain the power of the Aeons have a far longer and more treacherous trek ahead of them than ever before. The dreams of these Aeons have changed as well, bringing with them some rare new creatures. (Creating minor Aeons is allowed, based on Monsters and other Espers. If you have other ideas, talk to a staffer.)