They do, to an extent (though I very rarely drink coke). I tried a chai-based and cocao-based coffee alternative which had slightly more caffeine than decaf coffee, and it still gave me the same symptoms after a second cup. I guess my body just metabolizes caffeine differently than it did.
This rings very true. I tried coffee one time after quitting and the withdrawal migraines came back the next day like I was back in the thick of it.
I haven't had caffeine since then.