There are slight differences between an Orangery and a Conservatory. Besides the rich history of the Orangery,  its design is more akin to a room extension to your home. Generally, it has a flat roof instead of a Conservatory styled pitched roof. Additionally, some Orangeries contain a brickwork base instead of the Conservatory's use of its space for windows.
With modern Orangeries and Conservatories, the differences have narrowed even more.