For me, concentration is not the same as mindfulness. It seems that while concentration may actually be a prerequisite for mindfulness, it is only an initial step. My mindfulness includes an embodiment of the object of concentration. Concentration is a focus of my attention, an activity of my mind. Mindfulness is a focus of my whole being, my whole body and all that is involved with me being me. Mindfulness is for me a full body/mind engagement, an experience, more than a simple mental activity.
It has been a struggle for me to understand the practice of reciting the 5 and the 14 Mindfulness Trainings, also traditionally called Precepts. The recitation alone is not an engagement, and does not seem to be connected to mindfulness. I can see that mindfulness might lead to, even be a precondition for the Precepts. But focusing on the Mindfulness Trainings or Precepts is not mindfulness. It is more like checking a box that a task has been well completed.
Concentrating on the meaning of the Precepts may inspire ethical behavior. It may, more importantly for me, be a check whether I am behaving in an ethical manner. But focusing, reciting and concentrating on the Precepts is not an exercise in mindfulness.
I have for many years paid attention to improving my skill of concentration. That skill still serves me well. More significantly, I am now learning to fully engage my body/mind in frequent acts of mindfulness. Sometimes, the experience of mindfulness goes on and on. It is not an isolated engagement but a continuous engagement. It is so much more than concentration.