Architecture vs. Architectural Engineering from my understanding is the design aspect. From the architecture side it is more the design side of how a building may look, for example the aesthetics and spatial details of a building. The architects take part on designing the size, shape, space utilization and site requirements. They view the overall objectives of the clients.
While architectural engineers are responsible for the designing of the systems of the building. This designs would include how strong beams and columns need to be (structural specialty), what mechanical systems can be placed in the building and calculating the loads for the building pertaining to the amount of heat and cooling that will be needed for the building to the plumbing systems and fire protection (mechanical specialty). The final part of the engineering would be the communication and lighting of the building, setting up what wiring for all the outlets, lights, and anything else that would pertain to electrical needs (electrical specialty).
I completely agree with Jill's definition. To explain it in super layman's terms: Architecture is the design of a building. They make it look cool, pretty, *insert other adjective*, etc.. Architectural Engineering is making their design work. Architectural Engineers will make sure the building can support itself, will have enough lighting, keep the building cool/ warm, make sure all the plumbing goes to the correct pipe, etc. Architectural Engineers are typically the bridge from the Architect (or Company) to the Constructors.
Jill is correct; in its simplest form, an Architect makes the building look appealing while the Architectural Engineer designs various systems within the building (HVAC, electrical, plumbing, structure, etc.) allowing it to function properly.