In my experience, the biggest difference between a startup and small business is that a startup feels intense pressure to scale up the business before the underlying fundamentals are strong. There’s a “land grab” attitude wherein investors are willing for the business take on massive losses the first few years as long as the company is building a moat around what they’re doing that will be difficult for competitors to penetrate later on. The idea is to build as much of a monopoly as you can early, funded by investment dollars, and “turn on” the revenue streams later.
A small business, on the other hand, generally scales hiring/marketing/sales along with their current revenue growth. It’s a bottom-up approach to building a business, wherein you scale as your company’s fundamentals incrementally improve. My current company is a newsletter-based business where we’re making fun of the tech industry (https://www.techloaf.io) where we’ve kept expenses extremely low, only hiring folks as the business improves.
Both approaches can make sense, it’s just all about your goals (both as an employee looking for work at either or as a founder building a company).
So, a startup is a series of experiments with largely unknown outcomes while a small business - though still allowing for experiments and different approaches on a smaller scale - deals with more predictable outcomes.
That said, the question of "startup vs. small business" isn't a clear-cut dichotomy but often a continuum.
A small business offering a service can also experiment with addressing a particular market niche, for instance. This is a common theme for small / 1-person software consulting businesses.