I currently have the Blender 2.80 release candidate, and now that the official 2.80 is out, I was wondering if I need to download it again to stay up to date or if the release candidate is the same as the current 2.80.
Blender RC 3 and the official release of Blender 2.8 are not the same version. The last release candidate is a build based on commit 507ffee6e1f4 and the release version is based on commit f6cb5f54494e. That means there have been additional fixes between the release candidate and the final release.
In general it's best to update from official release to official release, unless you really need the cutting edge version. If you want to use experimental builds, be aware that bugs, compatibility issues and broken projects may happen.
Yes, you need to download a new version every time as there's no update option built into Blender. Hence, it's best to download a zip version e.g. for testing or wait a while. As to me, I wait for 2.81.