If it was about nature or concept of stuff...
Border is a thing that marks or separates two different areas. Sometimes, the difference between the areas are clear: the forest and the plains, the sea and the land, the city and the home. Other times, the differences are not as clear and the border itself becomes the differentiating divide: the border of one country to another, the border of sky and sea, the border of the rich and the poor. Oft times, they are both.
The gap between dream and reality. The divide between the living and the dead. The clash between ideals.
Studying the nature of borders seem to me to be studying the nature of that differences, how to recognize the change of areas, observing the differences, and noticing the divide.
Or maybe, even creating and enforcing a divide, or a barrier.
For doors, its nature is very closely related to borders. It is the established path between two areas whose borders are very firm. A door can be opened, closed, locked, guarded, or broken through.
Sometimes, you can also notice the reinforced door and instead choose to break through the less reinforced walls! (/jk /meme)
Compared to the study of borders, this seem more specific and focused, though seemingly actually part of the borders.
Doors are explicitly something that allows for travel between two separate areas, of entry and of exit, and of security between the two areas. The chokepoint of travel. Tolls and taxes oft are paid at the gates.
Create a door, subvert a door, break a door.
(Insert the Shining meme and the Do you want to make a Snowman meme here)