Solved the problem... when you use phpMyAdmin to EXPORT a database, if you choose EXPORT from the Main Screen, it will ask you which database you want to export (it will export ALL tables), and it will then add the CREATE command to the file, so that when you IMPORT it elsewhere, it will try to CREATE the same database with the same name.
The way to bypass this CREATE database, is to hit EXPORT from just about any other page except the main page of phpMyAdmin. In this case, you should get a list of all the tables in the database, and be able select which tables you want to export (any or all of them). When you go to IMPORT your file, it will NOT try to create the database, it will just import the tables into whatever database you want, even if it has a different name!
See this discussion on the phpMyAdmin forum: