Q:

With Fossil source control, does the "fossil clone" command have the exact same effect as if you just copy the repository file manually? 

With Fossil source control, does the "fossil clone" command have the exact same effect as if you just copy the repository file manually? 
Could I just put the repository file on a usb stick and transfer it to another computer instead of calling fossil clone? 

A:

No, it is not the same. 
Differences are:

User account control is per-repository.   
Artifacts such as private branches and their contents are not pulled
Everything that fossil scrub --verily --private would suppress is typically not pulled (see fossil help scrub)
Autosync URL is automatically set when you clone, creating a dependency link.  Of course you can set it later with fossil remote-url

But if you use the repositories for your personal use on both sides you can just copy the repository, there is no problem doing a simple file copy.  In order to merge your repositories, do not copy the most recent to the oldest, but set the sync URL and do a sync between them.  It is quicker and safer as it will merge changes made on both sides, preventing any loss of changes.