I have seen other people who have this conception of meditation, but I am not sure it paints the whole picture. Among the different schools of meditation there

I have seen other people who have this conception of meditation, but I am not sure it paints the whole picture. Among the different schools of meditation there are both those that tend to "suppress thoughts" and those that simply observe whatever arises. In the first category I would put techniques which teach you to focus on a meditation object, most often the breath or a mantra. If someone says "mindfulness meditation" I generally think they are referring to this kind of meditation, and examplars can be found in books like Mindfulness in Plain English or The Mind Illuminated (even though there are also both quite different approaches to meditation, one being focused on "insight" first and the other based on "concentration" first). They don't teach you to suppress thoughts, but they teach you to focus on a particular thing and IGNORE thought, which has the effect, long term, of causing those thoughts not to arise. But there are also schools that focus on "open awareness" or "just sitting" styles of meditation. This is very common teaching in Zen Buddhism but is also practiced in some schools Tibetan Buddhism, at least in Dzogchen. This, I think, is what you are referring to; where you sit and observe at a mental distance whatever thoughts arise. Eventually, this also causes thoughts to arrive much less frequently. If you are referring to the research literature, however, I think mindfulness generally refers to the first kind. As with everything, the borders blur together.