That is an interesting question and I think it is open to interpretation. My definition of a classic film is a movie with high quality acting, screenplay, direction, and all of the other facets that make a movie timeless. I think people usually define a classic film by its age. For example, "Mullholland Drive" (first movie that came to my head) may not be a classic based on its age, but it definitely has the potential to be one. I myself have defined a film as "classic" based on it being made in a particular time period (usually pre-1970).
I have not thought about defining films as being studio-era or Production code-era, but it more clearly identifies a distinction in time where the construction and presentation of films (especially screenplay) were abruptly changed. I love Production code-era films myself, so I will keep that terminology in mind in the future for sure.