For some, this post might seem like nitpicking semantics. But in a place like Manhattan with so many restaurants, I feel it is important to have some specificity in describing the variations of cuisines being served. For example, I find it wrong to classify Jungsik as just "Korean", Kin Shop as just "Thai", or Junoon and Devi as just "Indian".
Anyway, below are my personal definitions, would love to hear what everyone else thinks.
Modern/New/Haute to me generally refers to refined takes, plays, and variations of classic cuisines using modern global ingredients. It is the modern application of classics given the globalization of the world. To me, everything David Burke does is the exact definition of New American. Some places call themselves New American when I think they should actually be classified as Eclectic.
Fusion to me relates to the specific combination of one (or more) region's cooking techniques with another region's flavoring profile (spices, marinades, etc.).
Classic vs. Authentic
Getting dim sum in a crowded restaurant with people pushing carts is classic/traditional. Ordering dim sum off a menu is not inauthentic. Dim sum with lobster and lamb is modern, but not inauthentic. To me, a place can still do a modern take on a specific cuisine and still be "authentic".
Having said all that, I have no idea what to call Romera's cuisine.