I checked the two records, and they were indeed enumerated by the same man. I also checked the other families on these pages, and this seems to be the only duplication.
The two enumerations seem too similar to be of distinct families. If you can't find the parents or children of the second family in the 1880 census, I would conclude that it was the same as the first. Finding a record which identifies Bettie with Lydia/Lylia would clich it.
Your theory about the family having two houses is intriguing. Perhaps Elizabeth was the informant in the second case, which would explain the slightly different details. On the other hand, it's also possible that "Bettie" was Elizabeth's nickname, and the censustaker accidentally conflated the two women of the household into one.
These are the mysteries that make genealogy interesting!