Sigmund and Sigismund are different forms of the same name.
According to Wikipedia the name derives from Old High German sigu (victory) and munt (hand, protection). Tacitus latinised the name as Segismundis.
There are many monarchs with this name:
- A 6th century Burgundian king and Catholic saint who is known alternatively as Siegmund or Sigismund.
- A Holy Roman Emperor (15th century) named Sigismund of Luxembourg. The fact that he had also been crowned king of Bohemia, Croatia and Hungary might have contributed to spreading the name.
- Kings of Poland, Sweden and Lithuania, many other princes.
In the article on Polish king Zygmunt III Waza (as called in Polish) you can see that he signed as Sigismundus Rex. Thus, Polish Zygmunt and Latin Sigismundus are the same.
In German you may encounter various versions. The version Sigismund is, as far as I can tell without searching for statistics, no longer common as a first name, but exists as a name for historical persons. Siegmund or Sigmund are less outdated.