I don't think its another building, I believe what you are seeing are the actual windows that meet the interior, wheras the stuff they removed was built over it since glazing was in its infancy at the time and probably not weather tight. Kind of like windows facing an interior atrium
Strange that it would be in entirely different style than the rest of the exterior, no? I am surprised there are any windows at all there.
I'm also not 100% convinced the part they removed was original. First it looks closer to the po-mo interpretation of deco than the real thing, and second it matches those aforementioned phone booths so closely I'm suspicious. I am basing this entirely off the google street view, so I could be wrong. My guess is it probably had an understated geometric patterned glazing similar to the old Hancock, which was then redone to "improve" the building when they renovated PO square, similarly to how it is being "improved" now...
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Don't know how accurate this is, but I found it while looking for older pictures of the building (of which there are hardly any - it's like this building didn't exist until PO Sq park opened.)