Is it just me, or do they do the exact same thing?
Assuming you are comparing glBegin(GL_TRIANGLE_FAN) and glBegin(GL_POLYGON) they are not the same.
It’s just you.
Well, if you mean that a polygon can be triangulized into a triangle fan, then yes, kinda
If and how triangulization of polygons is done depends AFAIK on the OpenGL implementation.
I mean that when you look at the polygon as a wire frame, it is just made of triangles that all meet at the first point. The polygon doesn’t seem to work properly with complex shapes either. It was just an observation.