Great that this worked, Ben, but weird with the crash.
Convert vs Apply: take any image and open it Photoshop. (Use a copy, just to be safe)
Under “Edit” you will find both options. Use the Convert and choose any other profile, if the image is sRGB use the ACES CG for example. While you do that, have an eye on the Histogram. Normally it will change heavily.
Go back to the initial profile (which one it had while opened the file), you should get a similar result, the Histogram changes and the image on the screen should not.
With the same image, use now the Assign option and assign the “Aces CG” to an sRGB, the histogram will not change, but the image will look like the problem we have discussed above.
Why is that?
With convert, Ps tries to find values for each pixel to create the same appearance for the screen as before. With Assign (if the wrong profile is chosen, as described above) you just tell Photoshop to use the pixel-information and deliver it to the screen based on the profile. It will look not correct, except when assigned the only really fitting profile to it, any other profile and the image is unusable.
To answer your question now, why is there no difference? If you convert something from linear to liner, there will be no change, or sRGB to sRGB. If you assign a Linear to a Linear image, or sRGB to an sRGB “coded” image, no change of course.
Two more things:
The “Convert” option should be used when you understand all the options, to just click around might limit your quality. When you come from a huge color space (Gamut), e.g., ProPhoto, and the settings are not a good fit, then [perhaps] all values that will not fit into the new gamut of that profile (e.g, sRGB) will be changed, distorted or just (color-)clipped. To go back and fore with, e.g., “perceptual” will ruin after a while the data as well. So, being sloppy here—not a good idea.
The Assign option should be only used if you know what profile is the right one, as it translates the pixel-value to what is used along the whole pipeline, speaking of image pixels. (Data pixels, e.g., Depth, UV, or Normal-passes, etc, should not be profiled at all, and certainly not converted at any time.)
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I know that theme is avoided a lot, and lots of wrong information is available, especially when people dumb a LUT (Look Up Table) on top of it to get things “right”. Lots of misunderstood stuff; Too much to clear in one thread.
In Linear space, keep it linear and you should be fine. From where I look at it, sRGB as the smallest Gamut/Color Space should have no place in a pro-pipeline at all these days, and with UHD (REC2020) and ACES (Linear XYZ) now, things will change dramatically. (People love sRGB as it is close to REC709, but that is like working in 8bit/channel only to deliver a “show” in 10bit/channel, which is just a joke from my perspective). Quality needs care from the start.
I hope that was not too technical, but I hope the Histogram exploration will clear the difference. Profiles are useful, and any pipeline without color management will screw up, soon or later. Not advised, not wanted, of course.
All the best