The BC Libs are called that because of their deep ties to the Federal Libs, politically and personally. Influential Liberal MP Joyce Murray used to be a provincial cabinet minister under Gordon Campbell. She is also best friends with Christy Clark. Oh, and Christy's ex-husband is a prominent Federal Liberal strategist. It goes on and on -- those are only a couple of examples.
You're getting hung up on ideological differences, whereas in politics it's about getting and keeping power and influence.