Publishing means to put your site on a server in such a way that they are accessible to public. Anyone who know the site URL can come and see what you have.
Setting up a site more or less means the same thing. But you can say that a site can be "setup" even in standalone machine. It is then published for public viewing.
There is nothing like publishing a hosting account. But setting up a hosting account means creating a separate area on the web, accessible only through a username and password and to manage one or more websites and ancilliary services like email, FTP, databases, etc.
@ sukhdeepsinghkohli: Setup fees on shared hosting is to "force customer loyalty"