There's a few reasons, among them to attract certain kinds of investors, and certain types of potential co-workers, and to mix with whichever crowd the "startup action" is happening in.

If you want people to think of David to the incumbent Goliaths, something with a mission to introduce something new and breakthrough to the world, a conduit for the wild dreams of youth to come alive, call it a startup.

If you want people to think stodgy, established, nice stable place to work and pay your mortgage off for 30 years, but no changing the world, call it a business.

Like any branding, that will affect who approaches you and what opportunities you end up with.