Giant Stars including Supergiants and Hypergiants are stars that are larger in size compared to other stars including our own Sun. Our Sun is actually classed as a dwarf star because it is much smaller than some of the giants out there. They have a luminosity value of 0 and have an enormous mass. Luminosity is the total amount of energy that a star produces in one second.
Our own star, the Sun is a dwarf star compared to the really big stars that exist. Going by the picture at the bottom, giant stars are say 10x bigger than our own sun such as Pollux, supergiant stars are 100x bigger than ours and hypergiants are 1000x and above. Its a simplistic explanation based on the picture below. Their colours can range from blue (e.g. Spica through yellow (e.g. Pollux) to red (Betelgeuse).
The bigger a star is, the shorter its lifespan is. Being a giant star is a disadvantage when it comes to living, giants such as those mentioned will die long before Dwarf Stars such as Proxima Centauri which is tiny compared to the real giants out there. If you want to continue the human race, you would look to move to a planet orbiting a dwarf star rather than a supergiant.
The centres of Galaxies aren't super massive giant stars, they are super massive Black Holes. In the case of the The Milky Way, the galactic centre can be found in the constellation of Sagittarius and is imaginatively called simply Sagittarius A*.
The first stars that were created after the The Beginning of the universe were massive giant blue stars which lived fast and died young. The first stars in the universe would made mainly of supergiants or hypergiant stars that would as mentioned earlier, lived fast and died young. When they died, they would've been recycled into newer stars. It is said our Sun is a third generation star which means there would've been two stars in this area before our Sun appeared. Elements on the periodic table heavier than iron can only be produced by the heat and energy of a Supernova explosion. As they live and die and what gets born after will be smaller. 70% of all stars in the galaxy are in fact red dwarf stars so our Sun is one of the largest stars that is out there.
When people talk about the largest stars, they tend to refer to radius of the star, how many times the star is bigger than the Sun. The radius aren't precise and are scientists best calculations/guesses based on their observations. The stars are so far away which is why they are the best guess/estimations. Only by visiting a star will we ever know precisely just how large (radius) it is.
Massive stars are stars that are considered to have at least eight times more mass than the Sun. Mass is how much matter and weight it has compared to its size. UY Scuti might be the largest star, but its not the most massive. The most massive star that we know about is R136a1 and that has about 135 times the mass of our sun. Massive stars live fast, die young.
When a star has converted all its hydrogen into helium, the outward pressure on itself will beat the inward strength of Gravity keeping it together. The outward strength will win and the star will grow is size. Our Sun will one day begin to grow in size and will expand to include the orbits of the gas giants of Jupiter before it ends in a supernova and turn into a white dwarf. The good news is that there is still a long way to go before the Sun destroys the life on our planet. It is estimated that life on this planet has another billion years left, so still time to do the homework and get it marked. As the Sun grows, it will get hotter and the water will boil away but life will have gone before that. Stars like UY Scuti and Betelgeuse are hypergiant stars that are nearing the end of their lives. Betelgeuse is estimated to be getting ready to supernova in the next million years which might seem a long time but in astronomical scale of time, its soon.
There is a discussion on-going as to what is the biggest star in the galaxy, we can only talk about the stars that have been observed. The current biggest is UY Scuti, a star in the Constellations of Scutum. If you research the internet, you will find that some sites will say that the biggest is VY Canis Majoris or NML Cygni in the constellation of Cygnus the Swan. These stars are measured in terms of solar radii, a radii of 1 is the same size as our Sun such as Rigil Kentaurus also known as Alpha Centauri. Anything less that 1 will indicate it is a smaller star. UY Scuti is estimated to be about 1,708 times the radius of our Sun. NML Cygni, another contender for the biggest star has a radius of between 1,642 and 2,775 times the Sun.
The current largest known star outside the Milky Way is R136a1 which is a star in the NGC2070 Star Cluster in the Tarantula Galaxy in the constellation of Dorado. Its mass is once thought to have been more than 300x that of our own Sun and is far in excess of what astronomers had once thought was possible for a star. Over time, its mass is now calculated at being 265x our Suns mass. At that time, people thought a star could only be up to 150x the mass of our Sun. It is believed to be 10 million times brighter than our sun and has a temperature of 40,000 degrees Celsius on its surface. The star is more than 165,000 light years away. The light we see is what it looked like 165,000 years ago.
The largest supergiants such as UY SCUTI and NML Cygni tend to be red hypergiants which are end of the life stars when they've exhausted their hydrogen and are expanding near to their deaths. The star that currently holds the title of the largest yellow supergiant is HR 5171 in the constellation of Centaurus. Originally thought of as being a blue supergiant with a spectral type of A7V, the updated spectral type for the star as detailed in Simbad is G8Ia++B0Ibp making it a yellow giant star.
The Yellow Star has a companion star which according to E.S.O., the two stars are connected to one another. If this is true, the larger star could be a vampire star sucking hydrogen from its neighbour.
As you can see from the picture below, the giant stars tend to be blue or red. The hotter a star is, the more blue the star is. Stars like Spica is hotter than Betelgeuse which is a dying star and therefore more blue. A blue star will burn more fuel than a red star. You infer from the below picture that Pollux, a yellow giant star is about the same size as Spica taking the line that joins the two stars. The stars colour is also determined by its mass, blue stars will have extremely high mass compared to other coloured stars. Star colours are not static, blue supergiants can turn in red supergiants during their lifetimes and vice versa.