Habitica's primary website is at https://habitica.com/ but alternative sites are maintained for specific purposes. None of them are recommended for normal use.
All of the sites use the same database to store your data, so no matter which site you use, you will see all your tasks, party, quests, and guilds as normal. Your actions on any site will be recorded permanently as normal and will be synced to the other sites when you specifically use them.
The mirror site at https://habitrpg.herokuapp.com used to be an alternative way of accessing the main site. However, as part of the changes for the inaugural Habitica Naming Day, it was modified to automatically redirect users to https://habitica.com/. This was a necessary part of the DNS redirections that needed to be set up to allow the old and new URLs to coexist. The redirection was removed after a few years and the mirror site no longer works.
There used to be a beta site at https://beta.habitrpg.com, which was used by admins for testing new features and debugging new code for the game. It was not intended for use by other players because it usually contained partially completed code that could have produced wildly varying behavior and might have had many bugs. However many players were using it, so the site was decommissioned to protect them from incomplete code.
The beta.habitrpg.com host name is now a redirect to habitica.com, which means that anyone using beta.habitrpg.com will see the URL in their browser's address bar change to habitica.com.
The beta.habitrpg.com host name might in future be deleted entirely and will then not be usable.
Other test sites do exist at URLs that are usually not published. Occasionally, staff will announce that a new feature is available on one of those sites for testing by players. When that occurs, it should be reasonably safe to use the specified site for testing purposes, but note that there might still be bugs! These bugs might occur with the new feature, or with existing features that have been inadvertently changed when the new features were introduced. Players will be directed to log bugs on a specific GitHub ticket.
After the testing period is over, it will be very important that players return to the normal site so that they are not subjected to inconsistent behavior. Outside the advertised testing periods, the test sites will used solely by admins for testing incomplete features and debugging new code. Use by normal players could result in severe damage to the players' accounts, possibly including irreversible deletion of their tasks.