What is the difference between concentration and mindfulness practice ?

I am new to buddhism and meditation (I have been practising it for one month now), and despite finishing my fourth book on the matter, I am still very unclear about what a meditation session should look like when practicing either concentration or mindfulness. From what I understood, each of these practices are clearly differents and even have different pali names (Samatha and Vipassana if I am right ?). I can already tell that I can't differenciate concentration and mindfulness. When I focus on my breath, I am naturally distracted by all kind of things which I have to be mindfull of (the way my body feels, the sounds I ear, what I smell from the kitchen, my thoughts and emotions). And when I try to practice mindfulness, I can't help but focusing on my breath, because it is often the first thing that I can notice in that state, and it is always present. When I start my meditation I focus on my breath, then if something happens I try to be mindfull of it, and then I focus on my breath again until something else happens, switching maybe every 2 to 10 seconds. I am wondering why concentration and mindfulness are referred to as disctinct practices in the books I read, as it doesn't make much sense to me. At this point I am afraid that I may be missing something important.