The data itself will be quite separate unless you modify the design of the two systems to do otherwise.
The simplest way to keep department x from accessing department y's database and vice versa is to simply define different user passwords for the two files. The users will be able to see each other's file, but will be unable to open it.
With external server authentication or an opener file placed on each user's desktop, you could keep the two departments from even knowing that the other's database even exists on the same server.
Much appreciated. As it happens I've just found that Dept X the existing server is version 7 (hangs head in shame!) and the Dept Y files are from version 11. We're making plans to update the Dept X database to utilise Version 11 - there are probably *heaps* of new bells and whistles that the older data can enjoy :-)
Good news: version 7 and 11 use the same file format. Thus you can host all the files from the same version of Filemaker Server while you move forward to get all the clients updated to the latest version.