Partitioning discs with two OSs.

1. Partitioning the disk isn't going to sort the storage problem, if in fact that is an accurate recloning of space.

The Storage tab is known to report incorrectly. Also check by choosing your Mac HD and "Get Info" (command-i). It may be different. Try rebuilding Spotlight index.

How to rebuild the Spotlight index on your Mac - Apple Support

Some of the space may also be from Time Machine Snapshots.

About Time Machine local snapshots - Apple Support

Download Omni DiskSweeper:

https://www.omnigroup.com/more

DiskSweeper can give you a more accurate read of disk space than Finder or Storage Tab of About this Mac. It can also show you the precise size and location of all your files. It will inventory your disk starting from the files that take up the most space. If you want you can even delete files from OmniDisk Sweeper. But be careful some of the items may be important to your system.

2.You get Catalina by downloading the installer and when it asks where you want to install it choose the empty partition

Time Machine will backup if you make both Time Machine volumes in System Preferences > Time Machine.

You can drag and drop files between volumes.

You can't have both without partitioning, unless you want to use an external drive. I didn't mean to imply you could. I was just saying you need to sort the space issue first or you may not have the room.

To get Mojave you can download it here:

Get macOS Mojave.

Choose to install it to the empty partition.

I see this is a two-part post. 😎

Can I run 2 OS's on one disk or do I … - Apple Community

You can let the user know they don't have to partition the drive. You can create a new APFS volume. That's what I did the other day. :)

Hi dialabrain! I know it´s rude to butt in and “hi-jack” a thread, but your and macjack´s replies to the OP have caught my attention in a big way! I´m still running Mojave 10.14.6 on my 2018 iMac, and don´t want to abandon Mojave yet until I´ve played around and tinkered with Catalina. My idea is:

Create a new volume on my internal 500 GB SSD.

Install Catalina on it.

Then move, not copy, all my data (docs, Photos Libraries etc.) to the new Catalina volume.

On the Mojave volume I would have nothing but the System and Photoshop CS6. I depend on Photoshop for my daily work, and I know it doesn´t work in Catalina. Thus my idea of splitting my internal SSD into 2 volumes.

Needless to say I shall be making clones and TM backups of my Mojave setup before I start on this!

Am I thinking straight here or am I befuddled? Any help/suggestions gratefully received! Regards, Ian.

I guess. Even though you just reported one of my posts. lol

Installing macOS on a separate APFS volume - Apple Support

New APFS volume, that's news to me. Can you provide instructions?

Thanks, that helps. I will unreport you! 😎

Welcome. :)