Can iCloud download to one device but not another?

You can turn on, or not, iCloud syncing options on each device. See the options in Apple menu > System Preferences > Apple ID > iCloud (or if running a macOS earlier than Catalina, Apple menu > System Preferences > iCloud).

These manuals might be helpful:

How to free up storage space on your Mac – Apple Support

&

Add your Desktop and Documents files to iCloud Drive – Apple Support (section: Store your files in iCloud and save space on your device)

Yes, uncheck these boxes on your laptop in system preferences > iCloud if it is a pre-Catalina Mac or in system preferences > Apple ID if it is a Catalina Mac: