When deriving Gauss’s law in differential form (GLDF), $$\nabla \cdot \mathbf E = \frac{\rho}{\epsilon_0},$$ from Gauss’s law in integral form (GLIF) we get a tidier formula, which is however less general (to my understanding). In fact, while we can freely apply GLIF to point charges, linear charge distributions, surface charge distributions and volume charge distributions, we can only apply GLDF to the latters.

However, if we consider a point charge $q$ (placed at the origin of our chosen frame of reference for simplicity), we can define $$\rho(\mathbf x) = q \delta(\mathbf x)$$ and this makes GLDF true for point charges as well. In fact we are now able to recover GLIF in the case of point charges by integrating GLDF.

Is there something similar that we can do in the case of linear charge distributions and surface charge distributions?