I was able to come pretty close to your second attachment using a gradient map (which is where IAMSAM was heading).
If you search for "Photoshop Duotone" effect you'll find a number of tutorials. I've attached one below, which is what I used here, plus one extra modification. I followed the steps in the tutorial, but for my image I chose to greatly increase the contrast of the gradient map (where the black arrows are pointing, below).
Lastly, I copied the final image to a new layer and selected Filter>Sketch>Halftone, which gives the dot pattern. I set the layer blend mode to Overlay (but other blend modes also work well) and adjusted the layer opacity to about 35%.