Does 3rd Cousin 4 Times Removed Count?

My GG Grandmother was a third cousin to Abe Lincoln, which would make them Great Great Grandchildren of the same Lincoln back in the early 1700's.
Try to keep that straight in your head. I'm not 100% sure yet but I think my 5th great grandfather (Lincoln) was born in Massachusetts in around 1778.
Its a challenge to get focused on any family for the branches are many. I hope to get back to the Lincoln's soon. Interestedly at the time of 1850 census the town of Washington was in Lincoln County, Maine. Other towns in the neighborhood were Liberty, Freedom and Unity if that isn't a patriotic area I don't know what is. Branches of our tree lived in them all.
I found the "Vital Records of Washington Maine" compiled by Marlene A. Groves at the Godfrey Library in Middletown Ct.. In it Sarah E. Lincoln is married on March 9,1850. What is interesting and what makes makes genealogy so difficult is what you may find in a census. In the Washington Me. 1850 census Sarah E.(18) is listed as a daughter of James Lincoln and 9 days later we have our Sarah E.(19) listed with her husband Almond Newhall. It is easy to go off on a wrong tangent. Unfortunately neither birth was recorded.
P.S. I read another blog today with tips on researching genealogy and he talked about who might have given the info to a census taker and whether
they understood the questions. It makes me wonder if the two Sarah E.'s were the same person. If question about the families children was understood as "who are your children" and not as "the names of the children living in the house".