Stars are giant spheres of mostly Hydrogen (H) and Helium (He). In a stars core, nuclear fusion takes place which fuses these elements into heavier and heavier ones. Variable stars are stars that vary in their output of light, much like turning the volume of music up and down repeatedly. Within the branch of variable stars, there are many other types of these fluctuating stars such as pulsating and eruptive variables.
Pulsating variables are usually giant stars that repeatedly fluctuate in their brightness. Because these stars pulsate in their brightness, they also fluctuate in their surface temperature. The main type of pulsating variable is a Cephid variable. A Cephid variable is a pulsating variable star that consistently pulsates at the same rate every single time. Sometimes, these variables can fluctuate by almost two apparent magnitudes in brightness -for those not familiar with the term apparent magnitude, it is simply a way to measure the brightness of a star as it appears to us on our "pale blue dot."* The name Cephid derives from the delta Cephi star in the constellation Cephus. These types of pulsating variables are very important to our understanding of the cosmos because their pulsation period is directly related to their absolute magnitude, the apparent magnitude of a star as if it were only 10 parsecs (32.6 light-years) from Earth, which allows astronomers to easily calculate their distance from Earth. Cephid (pulsating) variables serve as a sort of cosmic yardstick.
Another type of variable star is an eruptive variable which is not as important to our understanding of the cosmos, but still very interesting. Eruptive variables are stars that experience a mild to catastrophic explosion which obviously alters their brightness and temperature. On example of these eruptive variables is a nova or supernova. When a close binary system consists of a white dwarf and another star, and the other star essentially ignites the white dwarf, it results in an explosion called a nova. After the initial nova, the star slowly fades. A larger version of this explosion is a supernova which is the sudden explosion of an unstable massive star. Unlike a nova, the supernova self-destructs an either leaves a pulsar (rapidly spinning neutron star) or a black hole.**
Both of these types of stars vary in brightness and temperature. Many times, these stars can be of the same spectral class, a temperature scale. Despite their differences, these stars are still essentially the same when it comes down to the basics of being giant spheres of Hydrogen and Helium gas held together by the universal force of gravity.
These giant spheres that we call stars vary in many different ways. In fact, there are many branches within the branch of variable stars that I did not go over in this essay for the reasons that it would add too many dimensions to an already technical essay. The types of variable stars all differ in important ways from one another, yet they still share the same common name -stars.
*Quoted by the world renowned astronomer and science advocate Carl Sagan in his book The Pale Blue Dot
**I do realize that in the third paragraph, I added a short extra compare and contrast, but it was due to the necessary explanation of the two