I think although relaxing is similar to mindfulness, there's still a marked difference. Relaxing is like walking as mindfulness is to exercising regularly. You may feel you've had some exercise after an occasional walk, but after regular exercise, your whole body feels different. I suppose someone can have a clear mind without it, but for those of us with unending chatter, worries and emotions flying in and out of view, it can provide a quietness of mind never experienced before and different from being simply relaxed. With practice, the clarity carries itself through stressfully situations.