Yes and no. Despite drawing from similar elements, the power source for Red Mages is technically themselves, while Black and White Mages use the aether around them as their power source. It's the same reason for the lore argument as to why Red Magic is supposedly weaker than Black or White Magic.
That being said, it's not just the basic lore that is an issue for Geomancer in the "GEO v. CNJ" debate, but it's to the point where they are carbon copies of each other. While Conjury claims to be all elements, it's effectively the three "natural" elements of earth, wind and water: the exact same as Geomancer. What Conjurers call "elementals", Geomancers call "spirits". Even the spellcasting is effectively identical albeit a couple of different words and a different choice of spellcasting focus. At the end of the day, I look at how Geomancer is portrayed in this game--not in any past game, JUST this one single game--and ask if it's different enough from Conjurer, and with all that I've seen, the answer is a big fat pile of "no".
Yes, you can ramble on about how annoying lore can be, but it's that lore--not the lore in any past game, JUST the lore in this one single game--that cements everything together and provides a reason for everything in the game world to exist in that game world. That's why I've been suggesting what I have been about Geomancer in that it should be like a master of magnetism or otherwise something unlike anything we've actually seen and even play off the original inspiration of the job (the Hingan Geomancers) as the Ishgardian Astrologians in that they'd be uppity snob characters putting the protagonist down who have no idea what they're doing.