Independet manufacturers of crafting material often publish conversion charts, indicating which of their supplies can be used as replacements for the ones promoted in crafting patterns.
As a service for their clients, craft shops or craft supply traders sometimes create conversion tables, even for conversion between the major brands.
There are also a lot of conversion charts floating around on the internet of unknown origin and accuracy.
Some might have been assembled by actual comparison of material colors, but they may as well be the result of on-screen color-guessing, matching of color-names or cut and paste from other sources.
There is no way to tell if the conversion table you found somewhere on the internet was manipulated by some evil yarn manufacturer from hell, or if it is even more accurate than some of the official conversion tables.
There aren't always conversion charts for every possible pair of manufacturers, so you might have to do several intermediate conversions, using several tables in succession. Of course the conversion error increases drastically with each intermediate step which makes the result even more unreliable.