When you simply do nothing, thoughts will stop on their own. When you clearly notice your breath, thoughts will also stop. There are more effective and lasting ways of achieving it. For example, knowing the true nature of the thoughts or making your mind happy & healthy.
Mindfulness refers to being aware of something. Mindfulness also refers to the capacity of the mind for knowing. Mindfulness can also refer to other things and can be interpreted in various different ways. If you wish to know mindfulness, it’s best to try mindfulness practice for yourself.