The five $d$-orbitals are classified into two sets based on their orientation relative to the coordinate axes:

1. Axial Orbitals ($e_g$ set): The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals have their lobes (electron density) concentrated along the axes. Specifically, $d_{x^2-y^2}$ lies along the x and y axes, and $d_{z^2}$ lies along the z-axis.
2. Non-axial Orbitals ($t_{2g}$ set): The $d_{xy}, d_{yz},$ and $d_{xz}$ orbitals have their lobes oriented between the axes.

This distinction is crucial in Crystal Field Theory, where ligands approaching along the axes cause greater repulsion to the axial orbitals ($d_{x^2-y^2}, d_{z^2}$) compared to the non-axial ones.