In Star Wars, the "New Order" refers to the empire formed by Emperor Palpatine at the end of the Clone Wars. In contrast, the "First Order" refers to the antagonist organization in the upcoming movie subtitled "The Force Awakens".
Please do not use these terms interchangeably.
Also, as a public service, anybody who wants to complain about how it's confusing that the thing that is older both in-universe and to us is called "New" while the thing that is newer both in-universe and to us is called "First" should consider this thread their official and only place to do so.
Also: have you ever noticed that we park on driveways, but we drive on parkways? What's the deal with that?