An infinitesimal element of length in the $z$-direction is simply $dz$, and similarly an infinitesimal element of length in the $r$ direction is simply $dr$. But, an infinitesimal element of length in the $\phi$ direction in cylindrical coordinates is not just $d\phi$, since this would be an angle and does not even have the units of length.

Using the relationship between angles (in radians!) and radius, the infinitesimal element of length in the $\phi$ direction in cylindrical coordinates is $r\,d\phi$. The same argument shows that the infinitesimal element of length in the $\theta$ direction in spherical coordinates is $r\,d\theta$.

What about the infinitesimal element of length in the $\phi$ direction in spherical coordinates? Make sure to study the diagram carefully. Where is the center of a circle of constant latitude? It is not at the center of the sphere, but rather along the $z$-axis. The radius of this circle is not $r$, but rather $r\,\sin\theta$, so the infinitesimal element of length in the $\phi$ direction in spherical coordinates is $r\,\sin\theta\,d\phi$.