A similar example of a DOE wrench with the same Circle-S logo (although, weirdly, a backwards die) on the shank, the same fractional size markings, and a similar model number on the flip side of the shank was posted a few years ago in the H.D. Smith thread as well the Old Logos Guide thread.
I posted this in reply...
The logo of an "S" in a circle was trademarked by H.D. Smith. Strangely, Starrett also used it, but only on pressed steel sockets. I am not familiar with either of them making DOE wrenches, though, which makes it even more odd. But those are the two I would search.
The "821" is also odd. It's not an ISN. It could be a model number, where the "8" is indicating the purpose of the wrench, possibly, but less likely, the composition, in a series of "8xx" model numbers, and the "21" is the ISN designator. It's an engineers' wrench, technically, and the markings (1/8" x 3/16") are correct for an ISN "21" wrench if they are expressed in U.S.S. nut and bolt sizes. The milled openings would be 5/16" x 13/32".
If you click on my name in that quote above it will take you back to the thread where you can see photos of the other example.
I don't have anything to add to the identification of the mfgr (other than to say I lean Smith due to their TM). But I will elaborate on the markings.
Note that the "625" model number on your find confirms my analysis. If the size markings are indicating the diameter of the threaded bolts and nuts (5/16" x 1/4") in U.S.S. standard, not the across the flats width of the head on the bolt or the nut, or the actual milled openings, it perfectly matches the Industry Standard Number (derived from Williams model numbering schemes) for a "25" wrench.
Here's a little chart to demonstrate what I mean and capture the two examples we have so far.
Note that Williams, and many other Mfgrs, would use a prefix in front of the ISN to indicate other characteristics of the wrench, usually its type. For example, Williams actually made 600 or 6xx series wrenches, including a 625, but they were checknut (or jam nut) wrenches, very thin in the beam with very thin heads. Your Circle-S "625" is not a checknut wrench. The "6" is indicating something else. Similarly, Williams made 800 or 8xx series wrenches, but they were not engineers wrenches, they were single box end. The "8" in
@PSCo1867 's Circle-S "821" is indicating something else.