Northern Flickers are large woodpeckers that forage mainly on the ground, feeding on ants.
Northern Flickers have two subspecies: the Red-shafted Flicker (C. a. cafer) of western North America and the Yellow-shafted Flicker (C. a. auratus) of the east and far north. 
The eastern yellow-shafted subspecies differs from the western red-shafted subspecies by having a brown face and throat (not grey) and the male's black (not red) malar.
This is the yellow-shafted (eastern) subspecies, and all four photos show a male (note the black malar).

1st, 2nd & 3rd photo: The Ramble, Central Park, Manhattan, New York City, New York, USA, 4 May 2014
4th photo: North Woods, Central Park, Manhattan, New York City, New York, USA, 2 November 2017