It sounds as if you are using the same Apple ID on both computers – and are synchronizing some things through iCloud.
In particular, it sounds like both computers are set up to store Desktop and Documents files in iCloud Drive, using the same Apple ID. If you have them set up that way, file sharing would be a feature, not a bug. This is meant for the convenience of a single person who has multiple computers (e.g., desktop and laptop) and wants to keep the documents on them synchronized.
Add your Desktop and Documents files to iCloud Drive - Apple Support
This is not the only form of iCloud sharing (synchronization) that might be turned on.
Apple recommends that each person have their own Apple ID, so if you are sharing a single Apple ID, the solution is for one of you to get a different one. Note that the person who is changing IDs may still have copies of data that is currently being synchronized - be careful not to remove these copies until AFTER disassociating the computer from the currently-shared iCloud account. (When things are synchronized, deletes will be synchronized everywhere, too, and you don't want to accidentally tell the system to destroy all the copies of data on both Macs and in iCloud.)