Matt Flegenheimer of the New York Times has an on-the record post on “off the record”. He writes that as as a national political reporter for The Times, “I have heard all manner of after-the-fact pleading from politicians who regretted their words.
“Politicians who insisted an on-the-record comment was actually off the record. (It was not.)
“Politicians who acknowledged that, yes, they’d said the thing they said, but what if we pretended they hadn’t? (Not how this works.)
“Politicians who promised unspecified future scoops, if only I’d convert their ill-advised comments from on the record to off the record. (No deal.)
According to the post, there is one caveat, “which cannot be repeated enough: There is no universally agreed-upon meaning for many of these terms — and The Times has no precise descriptions in its own internal guidelines — making it difficult to sketch out even working definitions. Let’s try anyway.”
The post also has a primer on the kinds of conversations journalists have with their sources, which you can find here.