Is it possible to backup one computer and not sync with another one?

You can sync iCloud Drive and iCloud Photos etc using your Mac Mini and only sync iCloud Drive on your MacBook Pro.

I am restating that instead of using the exact words in your post because you used the word "from" twice. When you sync, it is both directions (i.e., not just "from" iCloud). If you turn on an iCloud option (e.g., iCloud Photos, iCloud Drive, Contacts, etc) on two devices then the end result will be that iCloud and both device will all have the same data. In your example, if you have iCloud Drive turned on in both your Mini and your MacBook Pro, the iCloud Drive data from the Mini will be synced to the Pro and the Pro data will be synced to the Mini.

Apple offers iCloud Backup for iPhones and iPads but not for Mac computers.

It is possible to sync data from a Mac to iCloud if you turn on those options (e.g., iCloud Photos, iCloud Drive including the Desktop & Documents option). Syncing has some of the benefits of a backup (and the benefit of being offsite) but is not the same as a backup. Major differences include the fact that not everything on your Mac can be synced and the fact that if you delete something, accidentally or otherwise, there is only a limited time period (30 days in most cases) during which it can be recovered.

Synced data will be synced with iCloud and with any other Apple devices (using the same Apple ID for iCloud) where you have the same syncing option(s) turned on.

Also see: https://support.apple.com/mac-backup

And more information on syncing in:

Set up and use iCloud Photos - Apple Support

and

iCloud Drive FAQ - Apple Support