Windows requires you to have a monitor profile in order to have a complete color managed system. Check that you have assigned sRGB as your monitor profile, or that your calibrated profile is selected, and that that profile is set as "default".
In Photoshop Color Settings
- choose a working space. This can be essentially ANYTHING, most common choice is AdobeRGB or sRGB.
- in Color Management Policies choose "RGB: preserve embedded profiles".
- tick OFF all "ask when opening" boxes.
Now, when you e.g. process an image with Rawshooter Premium, choose "Colorengine camera profile" and RGB working space "Prophoto RGB", convert to 16 bit TIFF and open the TIFF to Photoshop, the color profile scheme goes like this:
- RSP applies "Colorengine camera profile" to RAW
- then passes the image though "Working space profile"
- Now RSP reads your "Windows monitor profile" and displays the RAW on screen.
In this state you edit colors and curves in RSP, the histogram you see portrays the color gamut, not screen colors. When you convert the photo to 16 bit TIFF:
- the RAW is passed though "Colorengine camera profile"
- then through "Working space profile" (note: NOT though "Windows monitor profile" at this stage)
- then it is saved on disk and "Working space profile" is embedded to the image
Now, you open that TIFF in Photoshop:
- Photoshop reads your "Working space profile"
- reads that image requests to use "Prophoto RGB" and it sees there is a profile mismatch. You have set PS so that it does not ask anything but preserves the embedded profiles, so PS opens the photo as "Prophoto RGB"
- and then displays it using "Windows monitor profile"
What you see on screen is not what "Prophoto RGB" is capable of (because no monitor can show full Prophoto RGB gamut), but internally all your edits are done in this large gamut of "Prophoto RGB" and histogram reflects that.
During the whole process above you see exactly same colors on screen in all applications.
When you print this image, you can choose between several methods of converting "Prophoto RGB" colors to "your printer/paper profile" so that colors available in "Prophoto RGB" are used to max. See
http://www.computer-darkroom.com/ps9_print/ps9_print_1.htm
If you send the file to be printed elsewhere, you will need to either let them know in which color space your images are on, or convert them to the profile they use (usually they provide a printer profile you can convert to).
So I'm not at all surprised that you are confused about colors space

Above "flow" is the most important thing in color management. Main point is to keep the image in as large color gamut as possible: to match (or rather exceed in small margin) the capabilities of the
best output device you have planned to use.
Choosing a profile is always a compromise, unless you have specifically calibrated all your devices. If you choose to have your photos in sRGB, other devices like printers will not get maximum color information, you get weaker colors which loose detail when you try to saturate them. If you use ProphotoRGB, you might edit some appearance on screen but might see very different colors when printing on a device that can handle larger gamut than sRGB of your monitor. That is why AdobeRGB is considered as the best compromise, it is not as small as sRGB and modern printers can output most of it quite well.
Here are some definitions:
Color spaceIndustry standard definitions of document color gamut.
ProfileComputer file which translates colors (between color spaces).
Camera ProfileThis profile corrects RAW colors to be more accurate. It does not do anything physical to RAW, it works on "realtime".
Monitor ProfileThis profile corrects your monitor colors to be more accurate. It does not do anything physical to files you view, it works on "realtime". You get most accurate monitor profile with hardware calibration devices like Spyder Pro, Monaco etc. If you do not have hardware calibrator, use sRGB and run Adobe Gamma.
Working Space in RSPThis is the color space you export the image to. In histogram reflects to the gamut of working space.
Working space in PhotoshopThis is the color space which is considered as default profile, it is used when creating new documents, and when saving files without profiles.
In normal RSP -> PS workflow it has no meaning, if "preserve embedded profiles" is on.Embedded profileThere are two ways to store profile info into image: embed the full profile as ICC data (the profile "travels" with the image), or embed the information what profile should be used (the profile must be installed on system before the photo is opened). Some converters like C1 Pro let you choose the method.
Color gamutRange of colors the color profile is capable of storing. When gamut is large, you can have deeper and more saturated colors in your image. Most monitors can display sRGB or little bit more, best monitors can show full AdobeRGB.
Convert to profileThis process reads the image colors and converts them to target profile. If the target profile has smaller gamut, then you loose colors for good.
Assign to profileThis command changes images profile information. If you assing sRGB profile to AdobeRGB image without converting it to sRGB (or embedding an sRGB profile with image and tagging that image to use it), you will see bleached colors because the assigned profile does not match the assigned (AdobeRGB) color gamut. In order to use assigned profile the viewer program must have access to the profile, unless profile is embedded (see "embedded" above).
Hope this helps.
(I wrote this really fast, so feel free to point mistakes)
Follow up:
https://photography-on-the.net/forum/showthread.php?t=121543