Hi Jimmy,
Thank you very much for posting here. This answer is a bit long, but your question will definitely be of value to other users.
The differences between the FREE and PREMIUM versions of the MSTW Bracket Builder plugin are outlined in this man page. In short, the free version is a texted based, requiring the user to input pretty much ALL the tournament data, including team names. The premium version is much more automated (brackets are updated based on results), provides more tournament options (double elimination), and offers more features in the front end displays (like team logos).
Now as to your question. I believe the referenced man page states that the MSTW Bracket Builder Premium version SHARES the teams database with the MSTW League Manager plugin. However it does not REQUIRE that the League Manager plugin be installed; it will provide the shared DB and admin screens to administer that DB. However, it does not allow you to enter teams as text outside the teams database, like the free version. Team names must be entered in the shared teams database, and then can be re-used. Team logos, home venues, etc are not required, depending on what features are used on the front end displays. The design decision that an extra screen or two required to set up a tournament is offset by the advanced front end displays that are available.
I hope that helps.
-Mark