You have two die varieties, not errors

SEGS is certainly a legitimate
TPG, they accept public submissions and they do have recognized experts on staff. The downside is their grades can be a little iffy on some coins and they have a tendency to overlook minor problems that are relatively market-acceptable(thin scratch, light cleaning, etc). For these two coins, I am in agreement with the stated grades
The code number listed is an old Fivaz-Stanton(FS) number, they are the authors of the Cherrypicker's Guide. The new number would be FS-25-1953D-601 and it has three different die states. You have the middle die state which is certainly clearer than the LDS. I believe that the "so-called" part comes in because it is not a simple overmintmark(OMM) but instead involves as many as five mintmark punches of Ds and Ss

. It is fairly clear on the EDS bust still takes a little imagination to see. The CPG gives values of $75 in MS60 and $150 in MS63.
The new number for the 1936 is FS-25-1936-101. It is a very tough doubled die with strong spread on IGWT, I can see the doubling clearly in the last photo. CPG lists it at $300 in EF40, the lowest given grade.
Two very nice
Washington quarter varieties
