What is the difference between a conservatory and an orangery?
From Google:

or·ange·ry  
/ˈôrənjrē/
Noun
A greenhouse where orange trees are grown.
Synonyms
hothouse


So, structurally speaking, there is no difference between the terms. The difference is merely based on what you put inside of it (whether or not you put orange trees in it). (If you grow lemon trees, is it a Lemony?)