I was given this in vector pdf format. When I create 3 squares each with the different formulas they all look different. Which do you trust to be the most true?
Ok, the question is this, are any of the swatch colors based on a conversion from one of the colors?
I.E. is the 143 C created by converting the CMYK and is the RGB created by converting the CMYK?
I would suggest that the 143 C on the to row was getting its RGB numbers from the same RGB icc profile as the one on the bottom row but a different CMYK profile.
Some colors just don't have perfect equivalents in other color models. IMO it's more of initial design issue. Logo designers are supposed to consider the equivalents right at the design stage. So you might have to show your client the subtle differences using your example.
By the rules of the ICC! () On multiple systems using the same application with the same color management setting. A Pantone color will convert to the same CMYK and RGB settings on all systems.
With that said, ICC conversions are not round trip. So the CMYK and RGB values obtained from the original Pantone colors conversion most likely will not convert back to the original Pantone color.
Regardless of profiles, some Pantone colors can't be output/manufacturered onto physical things from other color models.
That's true but conversions must be consistent for proper systems.