I’ve been practicing off an on for about ten years. I’m definitely not an expert. I like your explanation, but I think there’s more to it. Mindfulness doesn’t necessarily have to be about focusing on a particular thought. You can focus on nothingness and receive similar results. You can focus on a certain feeling for different results. Your focus object has a lot to do with what you get out of the experience. Additionally, the habit of recognizing what it feels like to not let your thoughts race can be powerful when your thoughts start racing at a later time.