Are there different philosophies or approaches to the game employed by certain teams?
Most definitely. You have your Neutral Zone trap teams which play tough defense and hope to beat you 2-1 (Devils, Wild, and Predators). You've got teams that play "fire wagon" hockey and try and score as many goals as they possibly can (Sharks, Caps, Canes).
You've got teams that go "stars and scrubs", putting out a killer first line and hope the bottom three don't give it away (Canucks, Lightning, Islanders, Ducks). You've got trams that are total team concepts, rolling four lines of nearly equal quality but without any superstars (Senators, Habs, Blues, Jets). You've got super old teams trying to go for one last run (Red Wings, Rangers) and super young up and coming teams (Oilers, Stars, Blue Jackets).
Watch a few weeks before throwing your hat behind one team. I'd still warn you off the Hawks, Kings, Bruins, and Pens. They are the best teams, but they are also in the middle of their runs. No one likes a bandwagon jumper. The first title is always the most fun. Gamble on a team trying to win their first in their current incarnation.