The "R" is for "replenishment" meaning, full stockpiles of expendables aboard. AOR are slower ships for carrying more goods--a supermarket, if you will.
The AOE is designed to be faster, and only with more immediate supplies--a convenience store of sorts, to carry the analogy.
The "E" in AOE refers to the major difference, AOE carry ammunition stores, vice the "reefers" (refrigerated coolers) on an AOR.
They also express a change in strategic application of UnRep (Under-way Replenishment) operations. Before, the thinking was to keep "fighting" ships together, and sort out the rendezvous of replenishment ships to the tactical needs of the deployed ships. That called for large ships--to cover many contingencies--what were slow-and-steady and capable of long, solo, voyages.
The thinking then changes to embrace making a stores ship part of a deployed task unit. This meant two things. One, the ship had to be fast enough to keep up, which meant a smaller stores capacity overall. But, that allowed the second thing--the AOE could be tailor-loaded to the specific mission specifications. As they were fast, a relief ship could take up station quickly--and, quickly enough to respond to mission/condition changes, too.
In addition, the faster ships actually allow for fresher perishables to be stocked, for better quality items for those deployed in the task group.