Sandra....My mother's 1909 bith certificate, which she brought to the U.S. with her in 1913, indicated Warsaw. When questioned, my mother would also reply she was born in Warsaw.Years later I learned she was born in Wierzbinek, some 150 km west of Warsaw. Many years later I learned the village where she was born was in the province of Warsaw at the time of her birth, but now was in the Wielkopolskie province.
When questioned where they were born many of our ancestors replied with the name of the nearest big city or with the name of the province which they knew would be more familiar to anyone asking.Just as when we who live in the suburbs of big cities here in the U.S. will give the name of that city when we're traveling elsewhere.
When telling me of Poland, my mother and grandmother always mentioned Wierzbinek, Ziemiecin and Sompolno, but at the time I didn't think they were important.I found the manifest of my grandmother, aunt and mother on the Ellis Island web site and it indicated they were from Wierzbinek (misspelled on the web site).
It's not impossible, but it is rare to find and confirm the name of the village where your great grandmother lived with just her maiden name.
To find records of your great grandmother in Poland you will need to know the name of the village/parish where she was born or lived.You can find that information in her U.S. records.
You don't give a time frame or when she was born or may have immigrated therefore it's difficult to give you definite information.The U.S. census records of 1900, 1910, 1920 and 1930 can give you clues as to what partition of Poland she was born, when she immigrated and if she was naturalized.Hopefully that will help you find the manifest of her arrival into the U.S.I did not find her on the Ellis Island web site with the spelling Kalwarczyk...she may have entered through on of the other popular ports such as Baltimore or Philadelphia.
If she married here in the U.S. the LDS FHL may have microfilmed the records of the church where she married and the priest may have not only written the name of her parents but the name of the village where she was born.
If she was naturalized (separately, not with her husband) her papers will give you the ports and dates of departure and arrival, the name of the ship and the name of the village.If not naturalized and alive in 1940 you can research her Alien Registration Form for this same information.
The fact the individuals you found have the same last name does not confirm they are of the same blood line.Also when contacting individuals in Poland it's important to know the name of the village, the name of great grandmother's parents and possibly siblings.