Lr desktop to laptop issues

Then the only images that can be shared are images that you place in regular collections on the desktop and share those collections. And unless you install Lightroom (NOT Lightroom Classic) on your laptop it will be necessary for you to access those collections on the web lightroom.adobe.com and sign in with your Adobe ID and password. There are some editing capabilities. However, it would be better if you installed Lightroom on the laptop.

It sounds like you are using Lightroom Classic (are you?) Please refer to Lightroom Classic as "Lightroom Classic" and not as "Lightroom".

Please read these instructions about using two computers with Lightroom Classic: https://www.lightroomqueen.com/how-to-lightroom-catalog-multiple-computers/

There is no sync between two computers with Lightroom Classic. There is the ability to sync between two computers using Lightroom. So again, we need to know exactly what software you are using.

When you refer to using Lightroom "CC" on your desktop, are you referring to Lightroom Classic or are you referring to Lightroom? There is a difference. Lightroom Classic stores images locally on the hard drive of your desktop, and only sends smart previews of images in collections that you choose to share to the cloud. Lightroom, on the other hand,  stores all images in the cloud. With Lightroom, you should be able to access images from both computers if you have logged in using the same Adobe ID and password.