Do you guys consider "franchise center" and "#1 center" to be the same thing?
Not at all.
Kadri is basically a low-end #1C at this point, but is definitely not the guy I'm looking to build my entire team around.
Franchise players are players that literally change the course of your organization (positively) and allow you to build around them as your centerpiece.
Many #1 centers happen to be franchise players, but not every #1 center (or #1 defenseman, or #1 goalie) is a franchise player.
Crosby, Malkin, Kopitar, Tavares, Matthews, Stamkos, MacKinnon, Bergeron, Giroux, Kane, Ovechkin, Doughty, Hedman, Karlsson - Those are franchise players, guys that you hang onto at all costs as cornerstones of your team. Barring extreme circumstances, you can generally expect most of these guys and their teams to be making the Playoffs more often than not.
Kadri, Backstrom, Kuznetsov, Couturier, O'Reilly, Draisaitl, Pavelski, Voracek, Kessel, Burns, Rielly, Carlson - These guys could all be considered #1s in their respective positions, but probably should not be your team's best player if you're looking to count yourself among the true contenders of the League.