My paternal grandparents were Jews born (as far as we know) in "Russia" - what is now Belarus. Here is what we know:
Abraham (Avram) Shechter, b. about 1877 in Homyel, by profession a tailor
Anna (Chene) Tileshevskaya, b. about 1880 in Cherykaw (Mahilyev voblast)
Both were Jewish. I believe they married before leaving Russia but am not sure. Chene left first, with a choir that went to sing for the Queen of England. When the choir returned, she did not. Abraham joined her later in England. I believe they left Russia in 1902 or 1903. Their first child, a daughter, was born in England. In June of 1905 Abraham left for Philadelphia; in January of 1906 Anna and Naomi (Chene and Nechame) joined him there. I have the ship records for all of them, both leaving from England and arriving in the U.S.