Different stars have different atmospheres.
All stars possess a so-called photosphere, which is the lowest and coolest part of the star's atmosphere - and as the photosphere is the part which we see with our eyes (hence the name) you can think of it as the surface of the star.
Above the photosphere, which ranges in temperature from around 3000 degrees to about 10 times as much, comes the chromosphere. This part of the atmosphere first cools down and then starts to heat up to about 10 times the temperature of the photosphere. Our Sun's chromosphere is the reddish ring that can be seen prior to the total eclipse. It is assumed that all stars have chromospheres.
Above the chromosphere lies the transition region , where the temperature increases rapidly on a distance of only around 100km. While all stars on the main-sequence feature transition regions and coronae, not all evolved stars do so. It seems that only some giants, and very few supergiants possess coronae.
The corona is the outermost part of such a star's atmosphere and is exceedingly - and surprisingly so - hot. The typical temperature is about 1 million degrees for a main-sequence star like the Sun, and about 10 million degrees for giants.
During a total eclipse, what looks like a crown around the Sun is the corona.
An unresolved problem in stellar astrophysics is the question as to how exactly the corona can be heated to such high temperatures. The answer lies in magnetic fields.