When you save an image using Save for the Web it converts it to sRGB and this will look different than Adobe RGB, and other color spaces. If you first convert the photo inside of Photoshop to sRGB, and then use Save for Web, then they will look the same.
The two following images show the difference if you do not first convert to sRGB before doing Save for Web.
Adobe RGB
sRGB
Cheers,
rfs