I think it depends on how your hosting account is set up.

My account is one public_html folder with multiple domains on it.
I this case I have one file-set, with one database, each domain will be assigned to its own template in the configure files.

It looks like there are also people who have a multiple file-sets each with its own domain assigned to it. I never used the multi-site this way, so i can not give any useful information about this method.