I can not update to OS Catalina 10.15.1 unless I have 10.15

I understand the terminology can be confusing. What you need to do is upgrade. Follow these instructions: Upgrade to macOS Catalina.

Follow all the instructions from Step 1 all the way through and including Step 7.

It sounds like you downloaded the Catalina patcher and not the Catalina installer. The patcher is for patching an existing Catalina installation. The Catalina installer is made for upgrading an older version of macOS or to install macOS onto a freshly erased drive.

Besides the directions @John Galt provided, you can also boot into Internet Recovery Mode using Command + Option + R which will boot an online version of the Catalina installer.

Make sure to have a good working backup before you upgrade just in case something goes wrong.

Use Internet Recovery Mode as I suggested.

Or as @John Galt suggested download the Catalina installer using these instructions:

https://support.apple.com/kb/HT201475

making sure to download the Catalina installer using this link (which is also mentioned in the article @John Galt and I both linked:

https://itunes.apple.com/us/app/macos-catalina/id1466841314?ls=1&mt=12

I can't explain the discrepancy. The only way to upgrade to macOS Catalina is to launch the app named "Install macOS Catalina". It looks like the icon in the screenshot below.

If that's what you have and that's what you did then I have no explanation.

What Mac do you have? Click on the Apple menu in the upper left, then About This Mac. What's listed in the window there?

Mine says: MacBook Air (13-inch, Mid 2011)

Yours should say something similar.

~Lyssa

Did you enroll in the beta program with this Mac?

https://beta.apple.com/sp/betaprogram/unenroll

~Lyssa