[sdiy] Filter topology: n-order == n-poles?

[Amos]

Hello,

I am reading Timothy Stinchcombe's analysis of the Korg MS-10 and
MS-20 filters, and was reminded of a question that's been in the back
of my mind for a little while.  Filter users typically refer to a
filter's number of poles, where each pole seems to add -6dB/Octave to
the cutoff slope.  Filter designers and mathematical types tend to
refer to the "order" of the filter, e.g. "2 cascaded, buffered
1st-order sections" in the Korg MS filters.  Is a 2-pole filter
necessarily a 2nd-order filter, or is the relationship more
complicated?  Thanks for answering this rather basic question...
thanks!

-Amos