I understand from Chabad's website, as well as my own Rabbi (who is Yeshivish) now that there is a difference between "Sepharad" and "Sepharadi" traditions and siddurs.
How do these differ? Who uses which?
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Nusach Sefaradi is an overarching name (much like the term "Sefaradi") of the Nusach used by Jews who follow Minhagei Sefarad (Spain) and Edot haMizrach. This is an oversimplification, but the intricacies of the differences between different Sefaradi/Mizrachi customs could fill volumes.
Nusach Sfard/Sefarad is the Nusach used by many/most(?) Chassidim, with the notable exception of Chabad. The Nusach which Chabad uses is very similar to Nusach Sfard, which is because (from my understanding) both Nusachim come from the Nusach that the Arizal used.
The nusach used by Jews of Sephardic extraction (meaning either Jews who live in Spain and Portugal, or are descended from those who were expelled from those places in 1492) is called "Nusach Sepharadi". This term has been (incorrectly) used to describe the nusach of those of the Edot Hamizrach (Jews from Iran, Syria, Egypt, Israel, and so on). It would be more correct to refer to the nusach of Spain/Portugal as "Nusach Sepharadi" and the nusach of other Sephardic communites as "Nusach Edot Hamizrach", and truth be told this is how it is today in the world of siddurim.
However, Nusach Sefard is an Ashkenazi nusach, formed by the Chasidim in 19th Century Europe. It was developed to blend the traditional Nusach Ashkenaz with the writings of the Arizal. It is best described as a cross-breed between Nusach Ashkenaz and Edot Hamizrach.
The reason it too is called "Sefard" is because the other non-Chasidic communities in Eastern Europe recognized the new nusach's "Sephardic flavor" and therefore began calling the new siddurim "Sefard". However it is important to note that any siddur marked "Sefard" is indeed a Chasidic prayer book.
(There are many variations of the Chasidic siddur, too, the Chabad siddur being one of them.)