Check Manage | Access privileges and see what accounts and passwords are defined. It sounds like you have the default setting: Admin with no password. Since no password is defined, you don't get a log in asking for a password. Try adding some passwords here and you'll see a change in behavior.
User Names (as set in the preferences) can be confusing, especially the way filemaker tries to use the current user name as the default account name during a log in. The user name setting identifies a specific copy of filemaker pro. You can access this text in calculations using Get(username) to identify the current user of the database--this can be useful in cases where your database is hosted over a network. You can also set a text field to automatically record the current user name when a record is created or when it is modified.