I looked again at the 1870 census and the passenger list and I am quite convinced that Henry and Heinrich are the same person. In 1870 his birth is shown as Hesse and Charles as At Sea. Charles would then have been born on the way to U.S. and Henry was 1 year old. So in 1870 when they show Henry born Hesse he would have to have to have been older than Charles, not younger so I think the 13 should be 18, that would make proper sense.Just a thought.
I tried finding the family in 1860 but no luck yet.
I found part of the family in 1880
1880 District 17, Baltimore MD
GROTH Mary age 45, widow works oyster house, born Prussia parents born Prussia
Frederick, son age 12, works oyster house, born MD parents born Prussia
Christopher, son age 12, works oyster house, born MD parents born Prussia
*** so on passenger list Mary is shown as Mary Elisabeth, in 1870 as Catherine and in 1880 as Mary again. I wonder what that was about.
By the way the passenger list was a transcription, not the original so it could have been transcribed incorrectly. I am going to see if the original is online.