The answer to your question is "no". It's not possible to have two computers, both using the same Apple ID, to save files or data to two independent instances of iCloud storage.
However, there may be more to your question. "iCloud" consists of several different features, including iCloud Drive, iCloud Photos, Contacts and Calendar sync, etc. You noted that "everything from the Air seems to have transferred to the Pro" and "I wanted to keep the two desktops different". It sounds like you are talking about the "Desktop and Documents" feature of iCloud. This syncs your Documents folder and your Desktop between devices, and it can be controlled independently of the other iCloud features. To turn it off:
- Go to System Preferences > iCloud
- Click the "Options" button next to "iCloud Drive"
- Uncheck the "Desktop & Documents Folders" box
- Optionally, uncheck any other app that you don't want to use or sync with iCloud
In this way, you can still have benefits of iCloud, such as Calendar and Contact sync, Mac App Store purchases, and a shared iCloud Drive space for files and selected apps, without having your Documents and Desktop folders synced. If you don't want any of those things, just sign out of iCloud on your new device, create a separate Apple ID, and sign in with that.