Moshe Shavit writes, 26 Aug 2004,
But Isaak and Aisik are the same name: theThis is true, but Itzik and Aizik are separate Yiddish names, although they both come >from the Hebrew name Yitzchak. My great-great-grandfather had a brother named Itzik, and another brother named Aizik. They were definitely different people.
The situation is similar to the names Jane, Jean, and Joan in English, all of which come >from John (originally >from Yochanan), but are now considered separate names. There are other examples of this among Yiddish names too, for example Yosef and Yospe. There is a Yospe on my family tree whose father's name was Yosef. The story I heard was that his parents wanted to name him after another Yosef who had died, but since his father's name was Yosef, they named him Yospe instead.
I think Shayna and Shayndel may be another example. I used to think that Shayndel was just a nickname for Shayna, but I noticed that my great-grandmother's headstone lists her name as "Shayndel," which suggests that it was not considered just a nickname.
I have seen it suggested (I think by the late Rabbi Shmuel Gorr) that Aizik does not come >from Yitzchak at all, but >from Isaiah, but this seems implausible to me.