Hey, sounds like you're familiar with some of the teachings. But mindfulness is not associated with samatha but rather vipassana in the western world, even though the most accurate Pali word for mindful abiding is sati. Samatha is classically associated with one-pointedness that can be a helpful adjunct to a practice of insight as the revelations that accompany a sustained insight practice can often be disturbing. Meditators steady their minds with the deeply pleasant states of jhana or near-jhana (laya) as base camps for insight practice.

If we look at the suttas, the Satipatthana Sutta, or Discourse on the Establishment of Mindfulness, offers a recipe to remain mindful of the sense aggregates to achieve insight:

"In this way he remains focused internally on the body in & of itself, or externally on the body in & of itself, or both internally & externally on the body in & of itself. Or he remains focused on the phenomenon of origination with regard to the body, on the phenomenon of passing away with regard to the body, or on the phenomenon of origination & passing away with regard to the body. Or his mindfulness that 'There is a body' is maintained to the extent of knowledge & remembrance. And he remains independent, unsustained by (not clinging to) anything in the world. This is how a monk remains focused on the body in & of itself."

The terminology is messy.

"Mindfulness of a thing" means samatha. "Just mindfulness" means vipassana. Sometimes they combine both and call the whole program "vipassana"...

Messy and inconsistent.

I like the terms "concentration" and "growing".

I think "concentration" is too strong a word, even, since samatha is really about letting go (of objects other than the object of meditation), rather than buckling down and trying to focus, which I think a lot of people associate "concentrating" with.

For me phrases like "gently staying with" or "quietly attending to" or even "remembering" (which is sort of what sati means anyway) work better than "concentration", but it seems like there isn't a perfect piece of terminology to describe the kind of effort/effortlessness balance that has to be achieved for samatha to work. But I feel that "letting go of distractions" is a better way around it than "concentrating one-pointedly" which tends to sound very effortful.

Mindfulness/vipassana/insight, I have no idea what a good phrase is. There are so many modifications of insight techniques that it's hard to find a common core sometimes.

That said, I believe the early Buddhist texts (i.e. the suttas) don't really make the samatha/vipassana distinction much if at all, this is a (relatively) recent development. And it seems like practicing one necessarily invokes some of the other (apart from during very refined states of samatha where there's no "bandwidth" for the kind of analysis and noting that happens in most insight techniques). I've often thought of vipassana practice as "applying the principles/mechanics of samatha to (xyz mental noting technique)", which might be why some traditions tend to have you do some form of samatha first before vipassana - because the mind needs a little training in being steady and dropping distractions before it can apply a vipassana technique in a (roughly) one-pointed way.

When I do the first one, I hold my attention upon the thing as perfectly as I can for a length of time

When I do the second one, I watch sensations come and go while refraining from moving my awareness in reaction to what I observe.

Is that what you do?

Mindfulness meditation is a term we use to describe the practices that certain famous/influential western meditation practitioners developed after coming back from the mostly theravada countries that they went to to learn meditation practices from the monks there in the 50-70s. Generally speaking, those practices were vipassana/insight practices, and so mindfulness practices are in essence, or at least are modified vipassana techniques. Mindfulness is the translation we tend to use for the Pali `sati`, mindfulness techniques tend to develop this quality of `sati`, which is a kind of re-contextualisation of your perception from "I am having an experience" to "an experience is happening within conscious awareness" in a direct, first person way. And yeah, the development of sati, along with other helpful factors, can help to gain insight, which is basically the way the mind looks at itself and conceptualises its own experience, in a kind of self-reflective way, and what it means to relax and tighten the tension that holding the mind in that way causes.

In these western teachings and in the theravadan writings, usually insight is contrasted with "concentration", which is `samatha`, which is a kind of effortless concentration on one thing. Focusing solely on the sensations of the breath at a point in your body is one way of doing samatha, or imagining a complex mental image (of, say, a mandala) or a simple image like a white circle. This kind of meditation is about dropping your attachment to everything except this one thing, which creates a strong attachment to that thing to the exclusion of all else, and this is often pleasurable because you're both strongly mentally attached to that sensation and it's a sensation that keeps happening at high "volume", which is very rewarding. With this you can enter states called `jhana` (which is actually pretty much the only word in early buddhism for "meditation", and through the spread of Buddhism, linguistically became "chan" in China, "zen" in Japan, and "seon" in Korea, "thien" in Vietnam...)

The reason that they are contrasted is because mindfulness practices tend to go the other way and include a larger scope of what you are including in your attention, for example mentally labelling what senses are being activated from moment to moment, or the sensations of the body/breath in a more wholesome way without blocking out external stimuli, but developing very strong clarity on the momentary aspects of those sensations and experiences, sort of applying a "samatha" style concentration to analysing the sensations as the "three core features" you described.

Both the approaches tend to suppress the "hindrances" in the mind that prevent jhana and insight. These are recurring thoughts and emotions that trouble you and stop this kind of mental configuration from happening in a stable way. The techniques use up mental and perceptual "bandwidth" in holding the mind in a way so that attention/awareness and holding on/letting go are balanced on whatever the object of meditation is. By developing samatha or sati, or a some of both mixed together, you can enter interesting and unusual states of consciousness that are pleasant, weird, intriguing, peaceful- that can be used as a point of inquiry into why the mind is grasping at things in certain ways and what the result of that grasping is doing to it.

> And yeah, the development of sati, along with other helpful factors, can help to gain insight, which is basically the way the mind looks at itself and conceptualises its own experience, in a kind of self-reflective way

Actually the insight of vipassana is pretty consistent in being other-reflective and not "self"-reflective. It's concentrating on mental states as they happen, and realizing that a mental state can never be truly "about" itself, but at most it can relate to the fleeting memory of a former mental state. Since there is thus no such thing as actual "self"-reflection, the next insight is that mental perceptions, at their most basic level, do not in fact evidence any continuity and distinct identity of the "self" - which is of course the core "insight" of anatta!

Right, by self reflective I wasn't talking about the self as identity - just as the mind and conscious experience noticing its own functioning.