It's interesting, because I myself love puzzles and am often disappointed by puzzle caches that are basically multis with virtual stages. That to me is more like simple task completion than puzzle solving (plugging numbers into an equation isn't much of a puzzle for me). Obviously the lines are a little blurry and these types of caches share characteristics with both listing types.
I also may be more likely to reference the cache page before searching for a cache than others. I wouldn't want to search for a Multi on my lunch break without knowing ahead of time about how many stages there are and about what the time commitment is. If I was just going by the nearest waypoint in my GPSr I'd run the risk of getting 2 or 3 stages deep into a 10-stage Multi before realizing it was an inappropriate choice for my opportunity window.
Alan2's excellent 1776 series is I think accurately listed as a Multi.