Page "Plane (geometry)" Paragraph 58

Differential geometry views a plane as a 2-dimensional real manifold, a topological plane which is provided with a differential structure.

Again in this case, there is no notion of distance, but there is now a concept of smoothness of maps, for example a differentiable or smooth path ( depending on the type of differential structure applied ).

The isomorphisms in this case are bijections with the chosen degree of differentiability.