Am I using the database I set up on my website or the one I set up with Store Manager? Are they one and the same?
Local database and remote (website) database are not the same.
Database installed with Store Manager is a kind of temporary database. It can be used for various purposes, one of most valuable of them is an ability to play with Store Manager functionality without applying changes to your live store (for testing purposes).
However you can use your local database to store your remote database inside it, make changes and then just synchronize your local and remote. So you can make changes locally and then upload them to the website database using Bridge connection. Working with local (Embedded) database is much more faster than working with remote one.
Read more how to work with Bridge connection and how to setup connection in Sotre Manager in our online documentation.