samatha contains sati [mindfulness], samadhi [stable attention], piti [joy], passaddhi [tranquility], upekkha [equanimy]).
vipassana is insight (among others) into anicca [impermanence], sunnata [emptyness], dukkha [stress], paticcasamuppada [interdependence of phenomena], anatta [no-observable self],....
The meditative states of jhana (dhyana in sanskrit, chan in chinese, Zen in japanese although the meaning has changed while the term traveled further east) originate from samatha practice.
Overall most Theravāda traditions or traditions that take the pali canon as a source kind of use this metta, samatha/sati, vipassana classification and acknowledge jhanas as meditative states. However, the meditation practice in the theravāda tradition was revived in the 19th/20th century only, so there is in the theravāda tradition no continuous meditation teaching lineage, so people had to make sense of the Pali canon source texts, which aren't exactly a meditation manual as we expect it today and there are concurrent approaches.
I am just a casual meditator (like 2-3 times per week) but overall an avid reader so I have seen quite a few different takes on how metta, mindfulness and insight meditation relate, most aren't dismissing one of these practices entirely, but the order and emphasis on when to practice what differ greatly. "dry-insight" is a I think to be understood as a counterpoint to voices that stated that a buddhist needs to practice concentration first and potentially even reach the jhanas before practicing Vipassana. So concentration / sati is not entirely dismissed. The idea of "dry-insight" is, that fewer meditation hours practicing concentration may be enough to develop insights and it is thus also advertised as a "quicker way" to awakening.
Overall, when reading or listening to meditation teachers, I am cautious about claims to "speed", which makes me a bit reserved about the Mahasi noting method crowd.
What made sense to me was: Laypeople should practice Metta meditation in any case. Practicing Sati (mindfulness) and Samādhi (concentration) is like taking your brain to the gym & spa, it should also help you a lot in dealing with stressful emotions, if your meditation object are your senses (breath, feet in walking meditation, hands while washing dishes) this seems to be a rather well-grounded activity and not inherently dangerous (unless maybe you have a serious psychological condition).
Proficient enough in Sati (mindfulness) and Samādhi (concentration), the route could go to practicing samatha and vipassana. Now my assumption would be that if you directly overemphasize vipassana and your skills for concentration, tranquility and equanimity aren't sufficient to contain reactions when 'insight' hits you.
That being said, Vipassana covers a wide range of stuff. Like "Body Scans" as done in Mindfulness based Stress reduction (MBSR) are thought of IIRC as vipassana practices, and IMHO they could just as well be thought of as sati practice.