Putting GWT or Closure in the same category as JSweet, TypeScript, or CoffeeScript obfuscates what these tools do.
Would you call a sed script which converted Java to ES6 via regexes a compiler, even though not an ounce of compiler theory was used?
I would define transpilers as a subset of compilers that are are only interested in high level language conversion.
It's the difference between say, translating books between foreign languages, and being an editor who rewrites a book to be better.
I'd argue that terms like "interpreter", "compiler", "decompiler", "transpiler", etc. are helpful for establishing a general taxonomy of program transformation tools, even if the boundaries aren't so clear.
As to your question, it doesn't really make sense for something to "change" from a transpiler to a compiler, any more than it makes sense to change from a Ford to a car. All transpilers are compilers; "transpiler" is just a little more specific. You know, like "gigantic" is a little more specific than "big", or "square" is a little more specific than "rectangle".
FWIW, I disagree with cromwellian that it's anything to do with optimization. I wouldn't personally say CPython transpiles Python to bytecode, but I'd also say an optimized transform from Dart to JS is a transpile. In my eyes, a transpiler is just any compiler where the target language is only intended to be written by humans.
(This changes over time, though. I'd probably not call Nim to C a transpile, although I might have in the past. We're probably reaching the point where X to JS stops being a transpile, too.)
You think that I can take a program, run it on some input in the past, and it's a transpiler, assuming that it fits the other part of your definition. Then I wait, say 10 years, run that same program on the same input and now it's not a transpiler?