Oh dear, I didn’t think I would do so much research at first. I had completely ignored the concept of the Profile Connection Spache, but then I started searching. I currently imagine the following:
The Profile Connection Space (PCS) is the superordinate reference that contains all colors that can be perceived by humans. It is standardized as CIE (LAB (Lab*) or XYZ).
The ICC profile describes the mapping from a color space to the PCS (source mapping) or from the PCS to a color space (target mapping). Tables for an interpolation and/or parameter series for a transformation can be used for the description.
If image information is to leave Photolab (saving an image file or printing the image), the Photolab wide gamut and the required/desired target color space must be calculated via the PCS.
Photolab provides an “internal” ICC for this purpose, which describes the mapping from the wide gamut to the PCS.
In addition, the printer interface is provided with the ICC that describes the mapping from the PCS to the printer. This ICC is determined with appropriate measurements for each output device and depends on various properties - paper type, ink, printer series, signs of ageing, etc. and is registered in the user interface by the Photolab user.
The software that processes the print output then does the following: Analyzing the source and target color spaces using the mapping information from both ICC profiles and then (in the vast majority of cases) calculating one defined mapping table(s). This mapping table(s) then allow both color spaces to be mapped to each other without multiple rounding errors.
This means that no conversion of image information from the source to the PCS and from there to the target is carried out, but the PCS is only used as a reference for the calculation algorithms from the source to the target.
This brings me back to my initial question: Who performs the conversion for the printout and what happens when files are saved?
I still assume that the corresponding printer driver of the printer manufacturer or another RIP software takes over this conversion task before printing. Photolab only provides the image information and the “internal” ICC at this interface.
Photolab performs the conversion when a file is saved. This is where two ICC profiles come into play: the “internal” one for mapping from wide gamut to PCS and the device-independent ICC profile from PCS to TIFF and JPG.
I’ll leave DNG out of the equation here, that’s certainly a topic in its own right.
The device-specific ICC profile, which is embedded to the target file, is then needed again when printing out the file to the target device.