Did the Buddha teach a single meditation that includes jhāna and insight, or do the scriptures have him separate meditation into different techniques? In what Buddhist traditions is it necessary to qualify meditation as vipāssana or samatha?
It is said in the scriptures that depending on the type of person, that person falls into the PATH in four different ways. That happens through insight (vipassana) and tranquillity (samatha). If a person listens to true Dhamma, take part in Dhamma discussions, and practise Samatha and Vipassana properly, dispassionateness with understanding definitely take place in him/her. That’s a given. If not so, then the fault is in that person. It is because of doing something which appears as correct thinking, or erroneously thinking that what one does is the correct thing. That is where the mistake is and not in the Suttas or in the Noble Eight-fold Path.
In the Yuganaddha Sutta (Anguttara Nikaya Sutta 4.170), it is said that insight (vipassana) and tranquillity (samatha) is developed in Tandem. In this sutta, Ven. Ananda describes the paths to arahantship by which insight (vipassana) and tranquillity (samatha) work hand-in-hand.
There are people in whom the other three ways may work. These three are:
Samatha followed by vipassana - after which the path is born in him/her;
Vipassana followed by samatha - after which the path is born in him/her; &
The mind stays fixed internally and become one-pointed - after which the path is born in him/her.
'Samatha' means 'tranquility' while 'jhana' is a certain degree of 'mental collectedness' ('samadhi' - 'concentration'). 'Samadhi' & 'samatha' are not synonyms.
For the most part, the suttas teach samatha (tranquility) & vipassana (insight) are developed in tandem (MN 149).
Thus for him, having thus developed the noble eightfold path...for him these two qualities occur in tandem: tranquility & insight.
Both samatha ('pleasant abiding') & vipassana ('focused on arising & falling') are fruits of concentration (AN 4.41).
In the Anapansati Sutta, each of the sixteen lessons (apart from the 1st two) has the words: "He trains himself", which means training ('sikkha') the mind in higher morality, higher concentration & higher wisdom. Therefore, vipassana occurs in the successful practise of each of these 14 lessons (as well as samatha in lessons 4, 8, 10, 11, 12, 14 & 15). For example, to concentrate on the breath will result in the breath calming (which is samatha; lesson 4) but will also result in seeing clearly the breath is impermanent & that the quality of the breath conditions/affects the quality of the body & mind (which is vipassana; lessons 3 & 4).