The Hasidic chants are called nigunim, singular nigun.
Not sure if there is much difference really between a nigun and a zmirah.
Hasidim were really like the Hippies of the Jewish world, or to be serious, what Sufiism is to Islam. Music and dance are an essential part of their lifestyle. It's a way for the common man to keep in touch with God.
In fact it often borders on an ecstatic trance.