It also means having instrumentation and observability as first class features. First party support for containerisation, the app needs to be robust and capable of handling shutdowns and multiple instances gracefully. In a cloud environment, when hardware fails or instances get resized, multiple containers may get spun up and everything is kept in sync through the database (or an external data store).
Authentication and integration with auth and secret providers are another distinguishing feature. I personally find "cloud native" software to be a pain to use locally because they usually come in the form of a docker-compose and kubernetes setup, and those absolutely gobble up ram and disk space.