Charles Carroll, abt1755-1836, who lived for a time in Allegany and Washington Co, MD, had no relation to Charles Carroll of Carrollton.
We know that in the 1820 Census Charles Carroll was living in MD with sons Jacob and David living nearby. Both Jacob and David had large families. Charles received a land grant in Montgomery Co, OH, and was living in Miami Co, OH, with son Jacob by the 1830's. Son John also lived for a brief time in Miami Co, OH, before moving to Indiana. Charles was killed in 1836. It is unknown what happened to David and his family.
Generally, my Carroll family tended to recycle certain favored names. I do not have any Randolph, Alexander or Christian Carrolls on my database. My family favored the names Oliver and Sarah, as well as the more common names John, Jacob and Mary. If you have any Olivers in your Carroll family that would suggest a relationship.
I would think it unlikely that one of Charles' sons moved to eastern Ohio (Jefferson Co) while Charles and Jacob went to SW Ohio! But I do not discount the possibility of a relationship. Good luck with your search.