I don't know how to make the colors appear the same when trying to Save for Web?
but I think it has something to do with this:
edit; the above is not the problem. I fixed it with this:
Unfortunately, it did NOT fix my problem in the first picture.
edit2; Fortunately, I solved the problem ! Aha..
http://www.viget.com/inspire/the-mysterious-save-for-web-color-shift/

but I think it has something to do with this:

edit; the above is not the problem. I fixed it with this:
Change the file permission to allow "Read & Write" then open the color profile with the ColorSync Utility. Change the "desc" tag to read "Coated FOGRA27" then save. Run the ColorSync Utility again and one of your problems should be fixed. I believe this issue stems from an illegal character in the "ISO" portion of the desc tag.
Unfortunately, it did NOT fix my problem in the first picture.
edit2; Fortunately, I solved the problem ! Aha..
http://www.viget.com/inspire/the-mysterious-save-for-web-color-shift/