Turbulent times in history led to many migrations of individuals as well as clans. My case was the Jacobite Revolution 1717 that brought the first direct blood relative of mine to America from Scotland. Then 1745 brought a bulk of the remaining clan over the pond. I was lucky that my family stayed in North Carolina throughout the centuries (and are still there). It made the research easier. The challenge has been finding that one person that fled while incognito (religious, legal or other difficulty of past life) to begin anew somewhere other than Scotland.
We all can't be directly related to the first few of the Mayflower passengers, unless they be cousins of some great-uncles half brother, as was the case with the first of my clan from the ship Blessing (second group to enter America). Close enough to call family but only a distant relative through extended blood lines.