Why do I have a third HD on my Home Page?

The description of your problem is confusing. In order to collect enough details about your hardware and devices please do the following and paste the information so we can see the details. These commands will list out all the possible disk mounts you have including network mounts:

Open Terminal

diskutil list | pbcopy

That will have copied the command output to your clipboard. Paste it in a reply.

Ditto, rinse and repeat with the following commands.

diskutil apfs list | pbcopy

mount | pbcopy 

system_profiler -detailLevel mini | pbcopy

What do you see in Disk Utility?

You should have an OS Volume, a Data Volume, and a Snapshot of the OS volume.

If you have more than those three things, you likely have an orphaned data volume from a reinstallation.

Select each Data volume and look at the Mount Point in the info window. If it is mounted to /Volumes, you can remove it.

The current data volume is mounted to /System/Volumes/Data.

Batestar backup 4 may be a volume on your internal startup drive that can be removed in Disk Utility.

First, check that there is nothing on it you need.

Then, select it in Disk Utility and click on the Remove Volume button ( – )

It still is not clear enough on the details, please run at least this Terminal command:

diskutil apfs list | pbcopy

You can copy the command line above to the clipboard and paste it into Terminal, and press Return. Then come back to this discussion and paste and the results will appear. This will let us know exactly what is going on with those 3 disk volumes on your internal drive so we can provide the proper advise on how to clean it up safely.

At this point, an educated guess tells me you have 3 APFS volumes on the internal drive. The internal drive is 1TB and you are confused by the size also showing 1TB for each of the individual volumes. Well that is because APFS creates a container and inside that container you have volumes and each volume actually shares the total free space between multiple volumes in the container. This is extremely useful if you wish to dual boot different macOS versions such as Catalina and Big Sur. You no longer need to allocate partition sizes, etc. You just create a second volume and providing you have enough total free space it all balances itself out in the end. It's also handy for the now read only System volume and read/write Data volume that appear in Finder as one volume. This is all APFS magic that allows for these new features.

External (Western Digital WD MyBook):

"BateStar 04 Backup" is an HFS+ Time Machine volume

Internal

"BateStar 03 11.3.x" is your primary internal macOS volume

"BateStar 03 10.11.x" is your previous internal macOS volume

"batestar backup 04" is perhaps a copy of one of the above or a copy of the Time Machine external disk volume

We need to know the APFS details of the 3 volumes on your internal disk. The screenshots don't show all the information.

As I stated previously, the batestar 4 mounted at /Volumes can be removed. The rest of them are the OS volume the mounted snapshot of the OS, and your data volume

Yes, a screen shot might help, showing “All Devices” in Disk Utility, and likewise the Terminal output of “diskutil apfs list”, or the above commands, thanks!