Help with connector part numbers
Those are headers and receptacles. 

The parts in the pictures look like the common 2mm battery connectors
made by JST. If those connectors will work then I would search
for JST and 2 pins and 2mm pitch. The exact pn's for the TH
parts should be


B2B-PH-K-S for a top entry header
S2B-PH-K-S for a side entry header
PHR-2 for a cable mount recptacle (without contacts)
The contacts are SPH-002T-P0.5L for the 24-28AWG crimp


You may want to double check those pn's at Digikey and Mouser.

Connectors are one place where all the search engines fall short.
The printed catalog can sometimes be a lot quicker.