I think that's close, but disagree with the uncertainty quantification bit. Often in both fields, you'll have a proof that "errors" converge at some asymptotic

I think that's close, but disagree with the uncertainty quantification bit. Often in both fields, you'll have a proof that "errors" converge at some asymptotic rate. Often in both fields, when you apply that tool to a finite data set, you don't know the error magnitude in this instance. I don't mean exact error, in the sense of 'if I knew the error, I could correct for it.' I mean you know big-O notation error, but not the constant factors. I do like the rest of the point you make, and it seems to match OP. Inference vs otherwise. Helping people learn/act/decide based on data data vs helping machines learn/act/decide based on data.