I feel that what most people actually mean when they say "compiled" vs. "interpreted" is whether or not the language specification has additional static checking beyond what is required by parsing. Essentially it is whether the language defers all errors to run-time or attempts to detect classes of them at compile-time. A language like JavaScript accepts as a program any string that parses, while a language like Java rejects many strings based on additional checks such as type rules. You can add static type-checking to JavaScript or Python, but it isn't part of the language spec. You can run C++ or Java with run-time type-checking, but it doesn't conform the to spec. In this way you could say that the language is fundamentally compiled or interpreted.

Of course, this doesn't address issues of incremental evaluation which often requires additional semantics for compiled languages.