S-Type Stars

S-Type stars are cool giant stars in the same region of temperatures and therefore colour as M-Type giant stars. What marks them out as different is that the amount of carbon and oxygen in their atmospheres are roughly the same. If the star has more carbon in the atmosphere, it is known as a Carbon Star. If the star has more oxygen than carbon then its just your regular average normal giant star.

The term S-Type star was first conceived by Paul Willard Merill in the United States in 1922. He came up with the term to class stars with unusual absorption and molecule bands due to s-process elements. S-Process is a series of reactions in nuclear astrophysics that is responsible for almost half the atomic nuclei heavier than iron hence the name for the stars. Wiki

It should be noted that the S is an upper case S. The lower case s in a spectral type means sub or narrow absorption lines and not indicative of the star being an S-Type star.

These stars are post-main sequence phase. Main Sequence is when the star is convert hydrogen into helium which is what our star, the Sun is currently doing. When all the hydrogen is used up, it will begin to use the helium to use as fuel. The helium will be converted into either carbon (3 Helium) or oxygen (4 Helium).

When it is in this phased, the outward pressure will be greater than the inward pressure of gravity  thereby causing the star to grown in size. The star will consume any planets that are orbiting it. Although Betelgeuse in the constellation of Orion  is not an S-Type star, it is believed to have consumed planets that were once in orbit round it.

Our Sun will one day begin its next phase of its life and grow. The new goods is that it won't happen for another billion or so years so there's still time to do that chore you have to do. It might become a S-Type star in the future but we'll have become extinct or moved to another world, the latter hopefully.

Example S-Type Stars
HR Pegasi
There are only three of these stars that are visible to the naked eye that were analysed by the Hipparcos space telescope. This star, HR Pegasi  in the constellation of Pegasus, the winged horse is just on the bounds of being invisible to the naked eye at a magnitude of 6.39 whereas anything with a higher magnitude is not going to be visible. In addition to being a S-Type Star, it is also a pulsating star but one with a poorly defined periodicity.