Is Being Mindful and Relaxed the Same Thing?
The short answer is "no".
Simply put, being mindful is being aware, and being relaxed is to be free of tension.
Being mindful is to become aware of how you are feeling physically, emotionally, mentally, and increasing awareness of your environment. Being mindful is tuning in to how you are experiencing the present moment and reserving judgment. That might mean becoming aware that you are pretty chilled out, or the exact opposite, maybe you're all revved up!
Relaxation is a whole different thing. Relaxation is the state of being free from tension. This could be physically or mentally.