Spheroid
A spheroid is a "squashed sphere"
Try different styles in this animation here:
images/poly-gl.js?mode=spheroid
A spheroid can be made by taking an ellipse and rotating it about its minor or major axis. Press play to see:
images/solid-rev.js?mode=ellipse
Oblate vs Prolate
The flatter one is oblate, the taller one is prolate (think "prolonged"):
Here are some more examples:

A watermelon is like a prolate spheroid

A discus is like an oblate spheroid

Planet Earth, our home, is squashed a little at the poles,
making it an oblate spheroid, but a very mild version of one.
Ellipsoid
An ellipsoid is the more general case of a spheroid.
- A spheroid is a specific type of ellipsoid that's symmetric about its polar axis (like a squashed or stretched sphere)
- An ellipsoid is the general 3D shape where all three perpendicular axes can have different lengths