Hi, Connie. There were several unrelated Smith families in Lyme, Connecticut (which includes places that were much later split off as East Lyme and Old Lyme) in the late 1600s and 1700s. I think you are getting members of some different families scrambled (goodness knows it's easy to do!).
For example, you (or whoever created the profiles) have given Samuel Smith-53698 two sons named Samuel who both lived to adulthood. That's confusing, but the older one has the wrong parents. Your https://www.wikitree.com/wiki/Smith-93726 is a dead ringer for https://www.wikitree.com/wiki/Smith-77583 (an ancestor of mine), who is the son of John Smith and his wife Mary.
Many of the church records have been lost, so there are quite a few people who don't appear in vital records. Donald Lines Jacobus published an analysis of some of the Smith families of this area some years ago, using deeds, wills, and similar records to help sort out the Smith families. ("The Smith Number," The American Genealogist, v. 25 (1949), No. 98, April 1949.) Some years before that my great-grandfather had correspondence with a local historian in Lyme who shared some local lore about the different Smith families of Lyme.
We can work this out (but this is all I can write at the moment).