4-4 point, double low approach, tenuki
It is rare for Black to play elsewhere in response to the 4-4 point double low approach, and allow to shut in the 4-4 point stone, because White gets superb influence while Black can only make small life in the corner.
at the 3-3 point is the canonical joseki typically given in Go textbooks.
The hane of is painful, but is necessary for life. See joseki-related life-and-death example 4 for more discussion on the life-and-death issues surrounding this position.
After , White can play elsewhere. In this variation, it is generally recognized that White is very thick, unlike the canonical joseki where White has cutting points.
Go Seigen recommended this sequence over the canonical joseki, which gives Black unconditional life with potentially more points while giving White cutting points. However, the life-and-death of this group is a lot more complicated than that of the canonical joseki, hence this sequence should not be recommended in high handicap games.
There are a few instances where Black chooses not to make life in the corner. In such cases, can turn the whole corner into White's territory.