What kind of wire-to-board connector is this?
Connectors of that style are known as MTA156 connectors. The pin pitch is 0.156 inches (156 mils). Several manufacturers support this type but the original was AMP which is now known as TE Connectivity.

The square pins of the headers are 0.045 inches (45 mils) in dimension.

Here is a connector image taken from the Mouser online electronics retailer.