Mechanically Valiants and Darts for a given year group are identical (except drive shaft length). Cosmetically there were differences such as body skins, body trim and interior surfaces. These differences were generally subtle, and are the only parts actually specific to a given model and year.
Many other mechanical parts are interchangeable corporation wide for a given year group, body platform, or both. This means many parts from a 1976 Dart, Duster or Valiant will fit a 64. Also, engine, transmission and major mechanical parts are not platform specific. Engines are substantially similar within engine families, meaning a 225 slant six from a 1980 Volare is a functional replacement for the 225 in a 1963 Valiant, and a 1990 318 is a functional replacement for a 1964 273. A 360 can, with minimal modification, replace a 273 as well.
Major mechanical sub-assemblies may interchange from one year group to another. For instance, the entire brake system from a later can will bolt into an early car yielding dual circuit disk brakes and a more common wheel bolt pattern. A V-8 engine and transmission will generally bolt in place of a slant six using all factory hardware, as such a combination was available from the factory.
In short, yes, most parts are the same.