They are completely separate, but chances are you have a connection string somewhere on instance #1 that points to the MySQL database on instance #1.
When you duplicated the instance, the same connection string would exist on instance #2 and it still points to instance #1. If you actually want each instance to have its own separate database, you'll need to make sure the connection string is updated every time it is cloned, (or else it set to the equivalent of 'localhost').