After the brainwashing and utterly worthless Strategy and Tactics course here at USNA, I'm still utterly unqualified to answer this question. But my understanding is that in the Global War on Terror, since the name of the game is no longer making the Russkies look horribly ill-prepared for a war at sea, the name change to STRIKE group is supposed to reflect the new mission of Carriers; putting lots and lots of warheads on bad guy foreheads. For whatever reason, Battle Groups sink other carriers, Strike Groups put bombs through windows.
It's also supposed to sound more aggressive. Whereas most assets in a Battle Group were sort of intended to defend the Carrier and it's air wing (destroyers hunting subs, cruisers firing SAMs), more of the assets of the Strike Group are also capable of joining in the strike missions. With Leahys and Belknaps gone (nobody else here at the Boat School knows what those are anymore, by the way), Ticos, Burkes, and the Improved Spruances (even if they're going away) can all carry TLAMs.
I guess it sort of makes sense. The old Carrier Battle Groups were meant to Battle their way to the Kola Pennisula. The new Carrier Strike Groups are meant to Strike a bunch of tents in the sandy parts of the world.
In summary: Battle Group + more Tomahawks - some Harpoons = Strike Group + NAMs for some staff LTs
Yes, I got an A on strategy and tactics. And I hate myself for it every night when I fall asleep in my rack.