Mobile Documents is just another name for iCloud Drive folder. There are all kinds of support documents for it, catalogs and stuff, and they use the alternate name.
If you do not have "Optimize Storage" turned on, then (unless you've specifically specified otherwise) the files in the iCloud Drive folder are on your Mac. The status of each file is shown in Finder:

In my case, I told iCloud Drive to keep "Album" always downloaded on my Mac, and I designated Rainbow to be kept off my Mac unless I clicked on it. (A photoslibrary isn't allowed in iCloud.) The other files are on my Mac (in the iCloud Drive folder,) and they are also at iCloud Drive at iCloud.com. If I want my file IMG_0109.heic, for instance, to not be at iCloud.com, then I would drag it from my iCloud Drive folder to some other folder on my Mac.
Here's the rule: if it's in the iCloud Drive folder, then it's (also) at iCloud.com. If it's not in the iCloud Drive Folder, then it's not at iCloud.com.
If you have "Optimize Storage" turned on, then some files (as shown in the Status column) may be removed from the Mac to provide extra room. Nonetheless, if you drag that file to another folder, out of the iCloud Drive folder, then it will be copied to your Mac and removed from iCloud.com.