It's not the terminology's fault that you didn't understand what "startup" meant (even to yourself) when you used it to describe your project. And if "startup" is indeed the correct abstraction for your project, why not use it? Finally, consider your audience when picking your words. Your family is likely to be more interested in what you're doing than the fact that you're doing it in a startup. You wouldn't tell the…
ALOT of people in this industry don't understand what the terminology means, at that rate..
Some innovative Fortune 500 companies are more of a startup or engage in more startup-like behavior than some self-proclaimed "startups" that have no idea about customers, market, and the discovery thereof.