Many (numbering) systems specify thread sizes. The basic classical methods are
  • length per mass (gives higher numbers for thinner threads)
  • mass per length (gives lower number fot thinner threads)
These methods can use different units like meters or yarns, have the decimal point shifted etcetera.

Thus far conversion seems just a mathematical challenge. As explained by the Klöppelstube and shown in a table by Bart & Francis. See also lacenotes on this subject.

But cotton, linen and silk have different diameters with the same weight and length. Above that the thread could have been measured with less or more moisture, loosely or tightly spun, measured before or after bleaching, you name it. So effectively you can't compare threads of different material or manufacturers just by the thread numbers.