Geometry is taken to be the study of distances and angles, hence the study of the metric. If we forget the metric, we still have what is called the smooth structure, and if we forget the smooth structure, we still have the topological structure.
Whilst the surface of a crayon is not metrically equivalent to the surface of a sphere, they are smoothly equivalent, and hence also, topologically equivalent.
Smooth equivalence, roughly speaking, allows deforming the object through squeezing and stretching so long as no creases or folds are introduced and furthermore no cuts.
Imagine the crayon was made out of plasticine, then we can easily see that we can deform this crayon to a ball, simply by squeezing it and rolling it up into a ball, and hence the surfaces are diffeomorphic. Its also notable here, that the bodies of the two objects and not just their surfaces are diffeomorphic. This need not be the case, for example a hollow sphere and a ball have the same surface and so are diffeomorphic, but the hollow sphere has no interior whereas the ball does, so their bodies are not diffeomorphic.