As I have learned in school and from wikipedia (also in Polish) coats of arms in Poland, and in the other countries of Europe, had been formed between 12th and 15th century. Their primary function was identification in the battle field. With time coats of arms became a kind of legacy transmitted from generation to generation. The coats of arms were described, according to strict rules, in so-called armorials (in Polish Herbarz from Herb - Coat of Arms). The term Herbarz is also used for genealogical registers of noble families in which there are included coat of arms. One coat of arms could be attributed to different noble families (different surnames).
So, to put it simply in "Cybulskis nobility" case, in 19th century in old Polish territory there were many Cybulskis families among peasants, townspeople as well as there wre two noble families. Those two nobles - Cybulski herbu (coat of arms) Łada and Cybulski herbu Prawdzic - were not probably related, lived in different parts of old Poland (in fact in two different countries at that time) and had different coats of arms.
I know it does not clear up the coat of arms subject entirely. If you are interested in the subject please ask more question and maybe we will be able to contact experts to address the broad subject.
Or maybe someone who has expertise in that area will find your questions in our Forum in the future..?
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