First let me say that both of the saw sets were patented in Vermont. Unbeknownst to many people, the Bennington and Shaftsbury towns were involved in both iron and tool making from early times. Eagle Square (later owned by Stanley) made iron squares in Shaftsbury from 1858 until the plant closed in 2001. Almost 150 years making the same tool in the same plant, a record that may never be equaled. The 1858 factory is still there and the local people are setting up a museum in the building.
The first connection deals with the Waste, Millington and Hutchins saw set (let's call it the WMH so I don't have to type as much). The Millington was none other than Norman Millington inventor of the Millington Graduator. The Millington Graduator was a patented device to semi-automate the marks on steel framing squares. This patent allowed Dennis George to form the Eagle Square company and put out of business or absorb all of the other square makers in Shaftsbury. Dennis George paid Norman Millington $5,000 for the rights in the 1850's. Norman moved to Bennington where he built a large and fancy house with the money. I have heard that there is a plaque on the side of the foundation explaining where the money came from to build the house.
The second connection deals with the stamp marking on the side of the WMH saw set. The saw set dimensions, holes and action match the patent, however the stamped marking says Corkins. The word patent is not stamped, but cast. Corkins was a rival square maker in Shaftsbury from 1851 to 1853, making squares under the Corkins & Draper name. The question is, did Waste, Millington or Hutchins work for Corkins or did they sell the rights to the patent? Who knows?
Finally, the WMH saw set is the first known plier type saw set patented in the US. At 660 it is early and survives because it was issued after a fire in the US patent office destroyed most patent records. It is possible that earlier patents were issued, but have been lost.
The third connection deals with the F. A. Parker Patented saw set. I have looked up the different Parkers in Vermont and I found only one which seems to be old enough to have patented this saw set and his name was Fredrick Appleton Parker. The patent witness was Dennis George, the founder and later owner of Eagle Square Company. I think that Parker may have worked for George and maybe Eagle square. I think that it may also be possible that George may have purchased the manufacturing rights and had Eagle square make them. The Parker saw set is hand made with hammer marks still showing on the flat areas. The squares made at this time were made out of iron flats hammer welded into the 90 degree shape. So the manufacturing technique seems to fit well with the Parker manufacture.