What is the difference between the two terms named "Eccentricity" and "Ellipticity"? I don't get the difference between the two terms named &quot;Eccentricity&quot; and &quot;Ellipticity&quot;, especially, in astronomy. I understand eccentricity as a measure of the curvature of a orbit but what is ellipticity?
Both ellipticity $f$ (also called flattening) and eccentricity $e$ are measures of how elongated an ellipse is, based on the semi-major axis $a$ and the semi-minor axis $b$  (figure from wikipedia).

They are defined respectively as
$$f=\frac{a-b}{a}$$
and
$$e=\sqrt{1-\frac{b^2}{a^2}}$$
For a circle, $a=b$, which implies that $f=e=0$.  In modern orbital mechanics, $e$ is used rather than $f$.  This is due to convention as $e$ is one of the six orbital elements Kepler defined.
Notes:

We can extend the definition of eccentricity to parabolic and hyperbolic orbits: $$e=\sqrt{1+\frac{2\epsilon h^2}{\mu^2}}$$ where $h$ is the angular momentum of the orbiting body relative to the more massive body, $\epsilon$ is the specific orbital energy, and $\mu$ is the standard gravitational parameter.  Then $e=1$ for a parabolic orbit, and $e&gt;1$ for a hyperbolic orbit.

While $e$ is conventionally used to describe orbits, $f$ is still used in astronomy as a factor expressing the oblateness of nearly circular bodies.

Here is a table and plot that illustrates the difference in values by fixing the semi-major axis $a=1$ and varying the semi-minor axis $b$ between 0 and 1.  Eccentricity and ellipticity are only equal when the orbit is either a circle or a line segment (when the orbit has no tangential component of velocity, in free fall towards the more massive body).