The difference is that the shadows are blurred rather than the highlights. I can't figure out how to do it in photoshop, but it must be simple.
Try setting the blur layer to Lighten blend mode.
Or to take it one step further, here's how I'd do it:
Duplicate your layer, convert the dupe to a smart object.
Run Gaussian blur on it. With it being a SO you can readjust the blur to suit. Set this layer to Lighten blend mode.
Duplicate that layer and set the blend mode to Darken and decrease opacity to suit.
Play around adjusting the blur radius and opacity of each SO layer till you get something you like.