There are two horizontal connectors in this illustration, one with four pins and one with six pins.
What are these connectors called?
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They are called crimp housings. Harwin makes them:
and they are widely available. I get the 10-way ones and cut them down to the size I need.
They are header receptacles. As pictured, they look like they could be constructed using header receptacle housings. In this case each attached wire would have an individual crimped connection that is then inserted into the housing.
They are generic "Rectangular Connectors" (....yeah). Digikey actually has a whole set of subgroups under the connector heading labeled "Rectangular":
Every manufacturer has their own line, with their own part number. However, searching for 0.100" (the spacing between pins) Rectangular connectors on a electronics component retailer's website should get you in the general area.