What happens to the beta version of an installed software when stable version is released?

Suppose I have installed beta version of a software and after some time stable/final version of the same software is released. What happens to the beta version already installed? Will it automatically upgrade to the final version if internet connection is available or will I have to uninstall the beta version and install afresh the final version? (Here when I say "software", I have a Linux operating system in mind.)