Are these the same families?

While researching a 3x great grandfather, I found two 1880 census reports that I believe enumerate the same family.  The focus of my research here is John Henry Clayton.  John Henry's first wife was my 3x great grandmother, Sarah L. Baxter.  Sarah died in New York between 1855 and 1859.  At the time of the census reports in question, he had been married to his second wife, Elizabeth, about 21 years and they had lived in Iowa for about 11 years. 

 

The census above is dated 1 June 1880 and records the residents of Sugar Creek Township in Poweshiek County, Iowa.  The John H. Clayton household is boxed in red and included John H., Elisabeth, Adel, and Floid F.  John Henry's occupation is recorded as hotel keeper.  Of particular interest to me are the birthplaces.  The family members were born in New York, as were their fathers and mothers with the exception of John Henry's mother; she was recorded as born in New Jersey.

The census above is dated 23 June 1880 and records the residents of 6th Ward, East Des Moines, Polk County, Iowa.  The John H. Clayton household is boxed in red and included John H., Elizabeth, Adel, and Floyd.  John Henry's occupation is recorded as hotel keeper.  Of particular interest to me are the birthplaces.  The family members were born in New York, as were their fathers and mothers with the exception of John Henry's father and mother.  His father is recorded born in New Jersey and his mother in Pennsylvania. 

I believe these two families are one and the same.  What do you think?