Wonderful Stirling engines you have there Danny, and a fine gentle restoration of your newer addition.
You are quite right to call these Stirling engines, but let me clarify that when some of us refer to them as "Solar Engines" we are in fact referring to one specific manufacturer who made several models of Stirling engines, and that would be "Solar Engines of Phoenix Arizona", many of whose designs are now made by PM Research.
Now they did make a solar powered Stirling engine which was called the "Sun Motor", and that PM Research now calls the "Sun Runner", so those truly are "Solar" engines and Stirling engines both at the same time. Well anyway, I hope this helps clarify the obviously somewhat confusing use of the term "Solar Engines" in reference to some Stirling engines.