The Swedish Nelson surname comes from the first immigrant, Nils Larsson, from Vollsjo, Sweden. Sons took their father's first name (Nils), their sons were named son of Nils or Nilsson. Daughters in Sweden also took their father's first name and were called Nilsdotter (Swedish for Nils' daughter). When they came to America, Peter, the son of Nils (Per Nilsson in Swedish) became Peter Nelson and that is how the name Nelson came to be the sur name.
Nelsons of Scots Irish descent arrived in the colonies around 1700. Thomas Nelson Jr. was a signer of the Declaration of Independence. Major John Nelson Led a regiment of the Virginia State Cavalry in the revolutionary war. There are similarities in the first names of males in these two lines. Because there is a Scottish traditional pattern of naming, it is likely that these two lines are related.