In Succah 8b I noticed two different wordings regarding a Succah:
א"ר לוי משום ר"מ שתי סוכות של יוצרים זו לפנים מזו -
הפנימית אינה סוכה
R' Levi said in the name of R' Meir: two craftsmen’s booths, one within the other, the inner one is not a Succah
And two lines down:
תנו רבנן גנב"ך: סוכת גוים, סוכת נשים, סוכת בהמה, סוכת כותים, סוכה מכל מקום - כשרה
The Sages taught:.. a Succah of gentiles, a Succah of women, a Succah of domesticated animals, a Succah of Samaritans, a Succah of any sort, is Kosher
Literally, in the first case, a booth is not called a Succah at all, in the second it is a Succah, but not Kosher. This pattern seems common in other Halachic realms also and, according to the way of common interpretations, is used interchangeably.
However, I was told that we should put close attention to the Sages' wording and there's a reason for such a difference.
So is there a difference and, if yes, what does it mean?