Sorry, but I strongly disagree with your explanation. It seems to categorize languages on the basis of what tools are available or widely used. That's not a property of languages.

A language can be designed once and then interpreters and compilers (and transpilers) can be made available for it.

Python is a classic example: it's most commonly interpreted, but can be compiled when performance matters.

C is usually compiled, but tcc offers the option to directly run it from source (-run).

History has given us both compilers and interpreters for various dialects of BASIC since the 80s.

Honestly I can't imagine why a language designer should decide upfront if the result of their study will be interpreted or compiled. And I have no idea what choices should they make to characterize it as a "scripting" language.