Stigma and Stigmatic convey the notion of a characteristic sign.
The roots point to stick.
The constellation containing stick includes sticker, sticky, steak, stitch as well as distinguish, distinction ... astigmatic, instinct, instigate ...
The roots of these notions are surprising - tiger, tigris, tigre point toward ancient Iran and the name of the regional river Tigris or Tigra.
Perhaps, getting wounded by a tiger left stigmatic streaks.
In Greek stochos as in stochastic emanates from the notion pointed or precise combined with the notion stake or stick. Also in Greek there is stizein for tatoo which is realized by the use of a stylus which in turn points to writing hopefully in good style.
Note Latin stilus, stigare, stingere as an English to sting. In Germanic we find stick.
To conclude, stigmatic implies a transformation of a sign into a signal - from a scratch we deduce a wound or mark by a tiger.
In medicine, faces become facies when they are stigmatic - for example, facies of Down syndrome. Another medical domain points to stricture, constrict, distinct, and extinct.
In science stochastic and stoichiometry convey notions of randomness and of measurement of atomic weights.