"Popular" means that Digg's promotion algorithm put the story on the
front page.
From among the stories recently made popular, a different algorithm
selects the "top" stories, and then presents them ordered by
descending Digg count. (The recency depends on the topic or
container selected, because some topics get more submissions than others.)
"Hot" is similar to "top": An algorithm selects "hot" stories from
the upcoming stories--those that have not yet been made popular.
Digg doesn't disclose those algorithms, but, obviously, they involve
more than just the raw number of Diggs.
>... you can sort by digg count for popular stories but not for top
>stories - is this a bug?
No, that's by design. Top and hot stories are always sorted by
descending Digg count, so the sort argument is disallowed.
We use these API endpoints to generate the Top widget on the Popular
pages and the Hot widget on the Upcoming pages. Those same widgets
are available to embed in your own web page:
If you build a Top 10 widget and examine the Javascript, you'll see
the API endpoint (called via our public API proxy, part of the
Services_Digg PEAR package).