I was reading Nakahara Chapter 5 and came across this paragraph:

"Clearly a diffeomorphism is a homeomorphism. What about the converse? Is a homeomorphism a diffeomorphism? In the previous section, we defined the differentiable structure as an equivalence class of atlases. Is it possible for a topological space to carry many differentiable structures?"

He then goes on to state that \(S^7\) and \(\mathbb{R}^4\)have multiple differentiable structures. I understand this has something to do with Donaldson invariants and Seiberg-Witten theory, but for now I'm just trying to understand physically/pictorially what a differentiable structure is and how it isn't unique. Is there an intuitive notion of how a single topological space can admit multiple differentiable structures?