The lore about Garlean Gunblades is that they use Ceruleum to power their gunblades.
Due to the lack of magical abilities the Garlean Empire discovery of Ceruleum as alternate source for magic allowed them to create their Magitek. The Azure Flames and blue color energy are the result of Ceruleum being used in their weapons and technology
The difference between Garlean Gunblade and Gunbreaker Gunblade is also due to what powers them as well. Gunbreaker Gunblades uses Aether Ammo which can be created by the user through their own magic thus providing unlimited ammo for the Gunbreaker to use for their Gunblade. Garlean Gunblades on the other hand use Ceruleum in their Gunblades to create Azure Flames for their attacks for both melee and range attacks.
Their combat use design is also different being Gunbreaker Gunblade is more defensive focusing on dispersing the Aether out of the ammo to create Magic Barrier so they can charge at enemies for melee combat or to infuse the Blade of the Gunblade for strong close range attacks or long range shock wave attacks but they can never fire solid bullets to harm enemies only to create magical barriers and infuse that aether released from the ammo into their blade thus all combat ability depends on the Blade only for Gunbreaker's Gunblades while Garlean Gunblade by design is more offensive focusing on utilizing both strong Melee and Range attacks by using the blade and infusing of Ceruleum into the blade for melee attacks and using the Gun Barrel aspect to fire power long range attacks that can create Azure Flame shots and explosions. This, however, prevents the Garlean Gunblade from having any defensive abilities as it is designed to be pure offensive.
The newest model of the Garlean Gunblade uses a Ceruleum Core to power its attacks so there is no need to reload the Garlean Gunblade. Gunbreaker Gunblade, by design and seen in the game cinematic, still requires the gunbreaker to load the ammo into the revolver cartridge part of their Gunblade.
You can basically compare the new Garlean Gunblade as a Semi-automatic Gun and the Gunbreaker Gunblade to be a manual Revolver