It's been my take that "startup" connotes something entrepreneurial, where "new business" (or "small business") connotes the start of something that's been done

It's been my take that "startup" connotes something entrepreneurial, where "new business" (or "small business") connotes the start of something that's been done before. That's a meaningful distinction to make because it involves different skills, a different assumption of risk, and a different level of tenacity needed to be successful in one or the other. So startup = selling something different. It's about pitching people your idea, and positioning a product creatively in the market. New business is about being seen (e.g. consider starting a franchise pizza shop and advertising on local TV/in print). It's "new" because people didn't know it was there before. But it's not "startup" for lack of its differentiation along the lines of how that something is sold. I like this defition because it permits that a new company that sells the same old product (e.g. Threadless and their tees) may be called a startup for its ability to creatively position their products. Exactly when a company transitions from "startup" to "going conern" is another question.