While there are many styles of eagles being used during the TR era, some distinct differences are from the way the head is faced, the way the wings are raised as well as the overall design.

Sadly there have been no official documents (that I know of) to explain what and when would a certain eagle be used for. One of the more detailed research has been done by Meda but he only focuses on railroad eagles and not those of political insignias.

JMO.