A press photo, also called a news photo, is the general term for a photo made by the press (newspaper, magazine news service such as Associated Press or UPI, etc). A wirephoto is specific type of photo made via transmitting the image via telephone line ('wire'). A wirephoto is a specfic type of press or news photo. People often use 'wirephoto' as the generic term, but it is a specific kind.
This is an article explaining wirephotos:
A Guide to Wirephotos
The empire state photo is an original press/news photo. You could also call it an International News photo, because that was the maker, as indicated by the stamp and paper tag.