colors changed on saved image??

The PSD file displays # after the file name, which means that it is untagged – it does not have a color profile.

The PNG file doesn't have the #, which means that it does have a color profile, probably sRGB.

So it seems that you have started out with an untagged image, which disables color management. If you create new files in Photoshop, always assign a color profile, like sRGB.

Try to assign sRGB to the original PSD file, by going to Edit > Assign profile > sRGB.

The colors will now change, and you may need to edit it to make it look right.

Then save as or export as PNG, and make sure to embed the profile. (sRGB). The PNG should now display identically to the PSD.

As others have said, how are you saving the image?  Are you exporting it for web?

Are you saving through Save For Web or Export? Both strip the color profile by default (how I wish they would fix that).

The file must have an embedded color profile to display correctly. Use these settings in Save For Web:

Or these in Export:

Then it will be consistent with Photoshop.

Note that some web browsers and many image viewers don't support color management at all. These will never display entirely correctly and a small difference to Photoshop is normal. In that case trust Photoshop.

No easy fixes and no point in showing us your color management settings - you are effectively not using any, hence your images get neither tagged on saving nor corrected on re-opening. Since it's a complex subject I would suggest you research it on the web. in your case it might be sufficient to set the proof preview to whatever is your monitor color profile.

Mylenium