Meaning of circularity in phase retarder definition

A phase retarder is generally some birefringent material used to modulate the phase of polarized light. A common example is a half-wave plate, which rotates linearly polarized light symmetrically about its fast axis.

Using Jones calculus, we can describe the Jones matrix associated with an arbitrarily-oriented retarder. According to the Wikipedia page on Jones calculus (https://en.wikipedia.org/wiki/Jones_calculus, see ‘Arbitrary birefringent material’), the Jones matrix is:

$J_{retarder} = e^{-ieta/2}begin{pmatrix}
cos^2theta+e^{ieta}sin^2theta & (1-e^{ieta})e^{-iphi}costhetasintheta
(1-e^{ieta})e^{iphi}costhetasintheta & sin^2theta+e^{ieta}cos^2theta
end{pmatrix}$

Here $theta$ is the angle of the fast axis relative to the horizontal, $eta$ is the relative phase retardation induced between the fast and slow axis, and $phi$ is the ‘circularity’, which for linear retarders is $0$, but can take any value between $-pi/2$ and $pi/2$ in general (for elliptical retarders).

My confusion: the circularity term seems redundant, after considering the presence of $eta$. Since the behavior of the retarder (its impact on the ouptput polarization state) depends on the relative phase change between field components along the principal axes, doesn’t $eta$ govern the ‘circularity’? How is the term $phi$ distinct from $eta$?