Hey, Guys - Sorry I've been absent for the last day or two, but between end-of-semester duties, preparing the house for Christmas, getting ready for a trip, etc. I simply didn't have a moment to spare. Anyway, I thought I better catch up with some of these threads that seem to have some loose ends.
@francklouis:
"...I still don’t have a clear answer to the original way back 4 pages ago, ..."
Actually, I believe you do. In fact, the answer was given to you several times, most recently, by Steve. The answer is that for the most consistent viewing of your images with different hardware and software, you must convert (not "assign") your image from whatever working color space you have been using to sRGB before you send it out for viewing by the general public, or printing at low-end print shops. To use Steve's words, "Period. End of story", LOL. The only thing I would add to this is that you do have two ways to convert to sRGB: You can either use "Save For Web" (under the "File" menu), or you can use the "Convert to Profile" (under the Edit menu) followed by a "Save As".
"...and now it seems we have another problem to deal with: What are websites doing to our images once we upload them. Do websites change the way an uploaded photo looks by removing the embedded color profile as the PSG website has done, and if that is the case how does one compensate so that what we see in PS-CC is what we see when posting to a website? ..."
The short answer is, once again, convert your image to sRGB before posting on a website. That way, even if the website / forum software strips out either the color space tag, or the embedded profile, or both, the worst that can happen is that the image turns into one with no color space specified. Such images, are, by default, always interpreted as sRGB, so, once again, if you uploaded it in sRGB, you will have no problems.
@MrTom:
re: "....Am I going about saving the profile with the PSD in completely the wrong way? (Or not as the case may be.) Is the checkbox for saving the ICC profile in the "Save As..." window a complete red herring? "
The topic of color space tags, vs embedded profiles is *REALLY* messy. Prompted by your question, I just spent the last hour or so doing some really detailed testing trying to determine which (common) software recognizes tags, which recognizes embedded profiles, with recognizes neither, and what does the software do if it encounters both, and what do they do when they contradict each other. Also, prompted by your question, I also looked at whether or not the "CMM flags" field actually tells us anything when it says, "Not Embedded".
First, the way to independently turn on and turn off ICC tags and ICC embedded profiles is using the two check boxes in "Save for Web", not the single color-space-related check box in "Save As".
Using the two different "Save for Web" ICC-related check boxes, it was trivial to see that they have different effects on the metadata. If you want to look at this yourself, just scroll down past where you were looking in EXIF_tool_gui, and you'll see that quite a few more lines at the end of the section that appear when you check "embed profile" using "Save for Web". The values for these fields (ie, the "tone reproduction curves") will contain values such as "curves" or "lookup tables" (aka, LUTs), depending on which method they used to embed the profile.
The really disappointing thing is that, like you observed in your experiments using the "Save As" method, the "CMM flags" never changed whether or not the image file actually contained an embedded profile or not. To be honest, I was shocked by this, but apparently, Adobe either doesn't bother to set this field at all, or else, they use it for some other purpose. Instead, when they actually embed a profile, it seems that they expect the receiving software to test whether the fields that contain the actual embedded profile data are present or not.
Knowing this, I re-checked the OP's images. His image #1 was tagged ProPhoto, but didn't have an embedded profile, whereas his image #2 was tagged sRGB, and also contained an embedded profile. For both of these, I "clicked through" to get the file that he uploaded, not the in-forum mid-sized preview, which could easily be different. I just didn't have time to do this.
Before I sign off, I'll just describe one very interesting test that I did: At least Windows 8.1's "Photo Viewer" seemed to display ProPhoto pix perfectly whether just the tag was there, whether just the embedded profile (but no tag) was there, or whether both were there. And, exactly as expected, the image looked absolutely awful when neither one was present (ie, so it interpreted the image as an sRGB). I did not see such consistent behavior in any of the other software that I tried with the exception of Firefox, with full color management turned on.
Now, I really have to sign off: I think that the OP has a clear, very definite answer (ie, "always convert to sRGB when an image is going out to the public"), but the more advanced, detailed points that you and I are getting into probably deserves to be put into its own thread and discussed separately. That being said, I am running REALLY short on time these days, so if we do start such a thread, I can tell you right now that my response time is going to be horrible, at least on and off for the next few weeks.
Best regards,
Tom M