There was a situation in my class where one person has asked "what's the difference between those two curves," (of a diagram, displayed on the whiteboard). One person has said "one is blue and the other is green," then the person asking the question has responded "it's not a difference, those are just two definitions." And maybe not my obsession about the definition of a definition I would just have ignored this occurrence.
I understand the concept of as a definition as a "class," a blueprint, to which instances (objects) of this class belong to. I also understand that definitions have no validity within themselves, they're just statements.
My question is, what did the person asking the question mean by saying "it's not a difference, those are just two definitions"? Where does the difficulty in understanding this concept lie? What picture do you have in your mind when you're trying to imagine the concept of a definition?
PS. I am aware of the diversity and structures of definitions. What I am interested in, is the essence of this concept, not its details.