Hi
When you calibrated your monitor you will actually have done two things. One - adjusted your monitor and created a calibration file to bring it as close as possible to a standard. Two -created a profile which is used by colour managed applications to adjust the displayed colours and make them as accurate as possible.
If you ensure you Photos are saved with an ICC profile, colour managed applications will display the image correctly.
Photoshop uses colour management - most broswers do not. They simply ignore the profile (Firefox can be set up to use profiles). Therefore comparing Photoshop to a non colour managed browser/viewer will show a difference no matter how good your calibration and profiling. The viewers without colour management are displaying incorrectly.
On older monitors with limited colours - an image in the the sRGB space did not look that different (managed or not) but on newer wide gamut monitors - correct colour management is absolutely essential .
Dave