Something that's unthinking is done without carefully considering how it might affect other people. An unthinking comment about your best friend's haircut might really hurt her feelings.
If you do something in an unthinking way, it's automatic or impulsive. Your unthinking prejudice against a certain breed of dog, for example, might be undermined when you actually meet a sweet Doberman. And your unthinking run through your Dad's flower garden to catch a football may instantly fill you with regret: if you'd stopped and thought about it, you wouldn't have done it.