@Autobadges
Let me try to Clarify some of your confusion:
"Is premium"
QB is a Program, just like Word or Excel. Word has Letters = data files. Excel has Spreadsheets = data files. QB has Company data files.
"allowing of more users and having all of the invoices and such"
And Such = Your Company Data file. Everything in in your Data file. The QB program is how you Manage that specific type of data file. Different QB Programs offer different tools and functions.
"on a dedicated server that can be accessed from anywhere on any computer that has the desktop version of pro"
The Server can be set up to Host the file. The individual Computers on your Hard-Wired network would each need to have QB installed, so that they have the Program. They will use it to Access the Hosted data file.
You would use Pro or Premier, for which program gives the tools you need, and Premier allows for more concurrent users to be in the same file at the same time.