I believe that, strictly speaking, Treasury tags are longish ones of which one metallic end is inserted into the other hollow end, whereas India tags are the shorter ones that have metal parts like crossbars at each end of the ribbon.
I cannot be certain, but my guess is that they took their names from the departments/buildings in which they were most commonly used. 'India' used as an adjective, as here, often referred to the East India Company, so perhaps tags of that particular type were commonly used in the company's HQ in London. By contrast, the Treasury may have tended to use the insertion-type for preference.