I didn't know that "nostalgia" means "home pain" (pretty close to "homesickness", really) or that the term was invented by a 17th century Swiss physician. According to [1], it was a calque from the German "heimweh", presumably because if you were a 17th century physician, your new disease wasn't proper until it had a classical name. (Edit: in fact, "homesick" was also a calque from the German "heimweh", according to [2]. So "nostalgia" and "homesickness" are cognate!)
The article doesn't make clear how the researchers distinguish nostalgia from simply remembering with emotion, which is not the same thing.