Dear WO'N: please forgive a small quibble, but it is not entirely accurate to say the Pilgrims left Europe to escape religious persecution. If I remember correctly they has been settled in Holland for about twelve years with no persecution.The thing they were most upset about is that they felt in danger of losing their identity and being completely assimilated by the Dutch. I was surprised on a visit to Plimoth Plantation a few years ago to see a map of how widely distributed over the map of England the homes of the Mayflower passengers were.
Could it be that the Saints were the group from Holland, and the Strangers were the ones who had not gone to Holland?

PS: I found a site which says the above is correct.