When I say "varying results" I mean that different views have different download options (any particular view always shows us either the 2 options or the 4 options)
I am assuming you are only getting the two option when you are trying to download a dashboard.
This is because you have to select which view in the dashboard you want to download data for.
This can be done simply by selecting a mark in the view itself.
Here is a brief article by Tableau Zen Master Andy Kriebel that explains it.
Thanks, Rody. That makes sense. (And, I figured out why one of my dashboards was offering me the data download option even when I had not selected a view in the dashboard -- that particular dashboard consisted of a table and a graphical representation of the same table, so there was no ambiguity about which data...)