Photoshop is color managed, which means it will convert to your monitor profile for display (document profile > monitor profile). Other applications that are not color managed will not do that and be less accurate.
Save For Web is a special case. As a holdover from earlier days when no web browser had color management, it displays without color management at default settings. That's the "Preview: Monitor Color" Setting. Change it to "Use Document Profile" and the two will display identically.
That said, this looks slightly off and I would suspect a bad monitor profile, probably from the monitor/laptop manufacturer.
Go to Control Panel > Color Management > Devices and set sRGB IEC61966-2.1 as default monitor profile instead of whatever's there now. Relaunch Photoshop so that it can pick up the new profile.
Thanks. It worked.
PS. One must note that to make "Add" button appear in the color management window, you need to check "Use my settings for this device." Otherwise it will be grayed out. So once I added the sRGB IEC61966-2.1 profile and set it as a default, Photoshop started showing all colors in a "matching" way with the rest of the OS
Yes, sRGB is safe and will always work - or Adobe RGB if you are among the few with a wide gamut monitor.
The whole mechanism of a color managed display in Photoshop is vulnerable. It really relies on an accurate monitor profile made by a calibrator - which is the proper way to fix a problem like this. But lots of people don't have calibrators. In that case sRGB is the closest.
What makes this a big problem is monitor manufacturers who ship faulty/bad/broken/out of spec profiles with the units, and why they keep doing that is one of life's big mysteries. These profiles never improve on sRGB anyway, quite the opposite.
But the real solution, as I said, is to get a calibrator.
Is it new function the Photoshop( Color Management )
No, it's been there since version 5 in 1998
But bogus display profiles from the manufacturers come and go. Right now it seems to be in fashion, judging by the number of similar threads recently.