I think the answer depends on the field. Let's crudely split economics into three major subfields, macro, micro and econometrics. . In macro, I think it's about the question, but in micro, much more about the methods. I'm less sure about econometrics. (Full disclosure: I'm an empirical macroeconomist).
Almost all macro questions are to do with either business cycles or long run economic growth. I'm sure there are exceptions, but I can't think of many. If you skim the latest AEJ Macros, pretty much every paper fits this taxonomy.
I'm struck by how often non-economists associate the term economics with, specifically, macroeconomics. And non-economists normally have a clear idea of what this means! I.e. stock markets, unemployment, inflation, business cycles, etc.
Macro tends to be quite eclectic in terms of methods, in either theory or empirics. One can easily think of top macro papers which are either heavily computational, using reduced-form applied micro style methods, using simple applied theory models, or much more complex maths (maybe this is a longer discussion for another time ...)
The kinds of questions which applied micro papers in top journals pursue is diverse. I can think of plenty of high quality applied micro work studying history, politics, institutions, gender, and a whole range of topics which are not traditional the preserve of economics. But there is a common strand to the methods -- high quality empirical work, with a focus on quasi-experimental tools and careful data construction. Angrist et al's credibility revolution was probably key to this dominance.
So there is a real micro/macro split. Macro clearly arranges itself around topics. Applied micro ranges broadly, with common methods.
I'm not sure here. But I think the line between stats and econometrics is blurry, when it comes to either questions or methods. I'm struck by how many econometrics papers could, or are, published in top stats journals, and conversely how many top stats journals publish useful econometrics. At my programme, there is a joint economics/stats PhD. I know several econometrics grad students who think of themselves as practicing particular kinds of statistics. So it is less clear cut.