The Difference Between The Sephardic Nosach (rite) and the so-called "Nusach Sefard"
To be sure, the Chassidim did not adopt the Sephardic nusach in its entirety, but rather modified the existing Ashkenazic nusach and incorporated within it many Lurianic formulae. The master Kabbalist Rabbi Isaac Luria known as the ARI, was himself part Sephardic and part Ashkenazic, however he was raised and studied in a purely Sephardic milieu. In essence, it can be claimed that the preeminent figure in the Chassidic movement is not the Baal Shem Tov, but in fact it is Rabbi Isaac Luria.
To confuse matters even more, different versions of this new hybrid called "Nusach Sefard" abounded. Various Chassidic groups have different versions of it. The founder of the Chabad-Lubavitch dynasty, Rabbi Shneur Zalman of Liadi (pictured third from top) was the first to publish a new prayer book "according to the rite of the Arizal", known as "Nusach Ari". However, as mentioned, his version was not accepted by all Chassidim as in fact being that of the Arizal.
In some parts of Eastern Europe, Orthodox Jews sometimes used the term 'sephardic' to distinguish themselves from their less traditional coreligionists. In Hungary, the election of a moderate religious Zionist, Rabbi Moses Glasner to the post of Chief Rabbi of Cluj, Transylvania (better known as Klausenberg) in 1878 precipitated the establishment of a newly formed “Sephardic” community in that city. The group consisted of about one hundred Chassidic families who decided that they could no longer remain subject to the authority of a Zionist Rabbi. The term “Sephardic community” was a sort of legal fiction designed to gain the recognition of the secular authorities that would recognize only one Orthodox community within a given town or district. The only “Sephardic” aspect of the community was that they recited prayers in “nusach sefard.” 
There were also many Ashkenazic Jews in Eastern Europe who adopted the Sephardic pronunciation of Hebrew because they felt it was the correct one, but we'll leave that for a different post.
A CHASSID OR A SEPHARDI?
The portrait (second from top) of Rabbi Shmuel Yaakov Falk (1710-1782), (I mentioned this enigmatic figure before in a previous post) known as the "Baal Shem of London" is often confused with that of Rabbi Israel ben Eliezer, the Baal Shem Tov and founder of the Chassidic movement.
An indication of the confusion that the misuse of the term “Sephardic” often engenders can be seen from the following example.
Former Chief Rabbi of Great Britain, Rabbi Dr. Herman Adler in his fascinating biographical sketch  of Rabbi Falk writes that Falk referred to himself in his personal book as “the son of Raphael the Sefardi”. However Adler is quick to point out that the term “Sephardi” in this case does not necessarily denote Iberian origins but rather refers to the (then) newly emerging sect of Chassidim who were often called “Sephardim” or “Anshei Sfard” because they prayed in a modified Sephardic rite. In a later republishing of the same article, Adler provides more clues as to the origins of Falk. This time no mention of his possible Chassidic connection is made. Adler merely wonders, “It is unclear why and how he (Raphael the Sephardi) received this appellation (Sephardi). Had he immigrated from Spain or Portugal?” and adds that “Falk's Sephardic pronunciation of Hebrew may have been due to his parentage”. Additional evidence seems to bear this out. In the comment on that passage, Adler writes that Falk gives his name in his commonplace book as חיים שמואל יעקב דפאלק מרדיולה לנידו (Chaim Shmuel Yaakov d’falk Mardiola Laniado) and wonders whether he might possibly be related to the Laniados, a Sephardic family that settled in Italy and the Middle East. The answer seems to be in the affirmative.
Falk’s Sephardic ancestry is also briefly mentioned in the recently published Mibaal Shed L’baal Shem (translation mine): “it seems that his father Rabbi Joshua Refael the Sephardi was a descendant of Marranos who arrived in Poland in the 16th century and retuned openly to Judaism. Additional information on Falk’s family is unknown”. 
AUTHENTIC SEPHARDIC CONGREGATIONS IN EASTERN EUROPE
However, there were authentic Sephardic congregations in Eastern Europe. Dr. Moshe Montalto, a Sephardic Physician who settled in Poland in the 17th century built a Synagogue in Lublin where the congregants prayed in the Sephardic (Spanish-Portuguese) rite. In Zamocz too, a Synagogue (pictured first from top) was established by Sephardic Jews who settled there in the 16th century and was still called the "Sephardic Synagogue" up until World War II, long after the descendants of the original Sephardic founder assimilated into the Ashkenazi community or moved out.
In Krakow, the historic capital of Poland, a community of Sephardic Jews, who arrived in Poland via Italy, maintained a separate existence until the middle of the 17th century. They kept their own traditions, including praying in the Sephardic rite and only marrying among themselves.
In Lithuania too, authentic Sephardic congregations existed. Shlomo Katzav in his booklet Hasefardim be'eretz Lita lists Sephardic congregations in places like Otian, Biraz, Dolhinov, Heidozishok, Vilkomir and Kopishok. Katzav lists several congregations with the name "Alsheikh" (in Horodna and Shavel, which probably indicate eastern origins). There are also two "Alfas" (indicating origins in Fez, Morocco) congregations, one in Tabarig and one in Lida.
Arthur Menton in The Book of Destiny: Toledot Charlap mentions one Lithuanian town whose Jewish community seems to have been founded by Sephardic emigres, namely Vilkaviskis (Vilkovishk). The community kept accurate records and as recently as 1920, a massive tome containing information about 400 years of Jewish life in Vilkaviskis was cited by several researchers. The book was unofrtunately lost or destroyed in the decades after World War I.
The book indicated that a Jewish settlement existed here at the beginning of the 16th century...Princess Bora Sforges made a gift of lumber to the community to build prayer houses and the copper domed synagogue known to its last days as "the old shul". Its ark... housed the profusely embellished Sefer Torahs which originated in Spain.
. For the background and more information about the reasons behind the secession see http://www.dorrevii.org/. I am indebted to David Glasner (a descendant of Rabbi Moses Glasner) for this inormation.
. The article is available in its entirety online here
. See Jewish Budapest; Monument, Rites History