I'd claim that the time ranges for these depend on what we're talking about. "I had a sandwich a while ago" is wastly different from "they had a child a while

I'd claim that the time ranges for these depend on what we're talking about. "I had a sandwich a while ago" is wastly different from "they had a child a while ago". "The other day" and "back in the day" might not differ as much but still...