How can red supergiants be cooler than dwarfs of the same spectral type? The Stellar Classification Wikipedia article has a sentence:

Red supergiants are cooler and redder than dwarfs of the same spectral
type

Which seems to be true, my course has a similar statement. However, here is an HR diagram:

Spectral Class varies on the same axis as Temperature (see top horizontal axis). Does the claim that &quot;red supergiants are cooler than dwarfs of the same spectral type&quot; only says that since they are in the same spectral type, their temperature is roughly the same, but the red giant is a bit cooler, or is there more to the story and I am misusing the HR diagram?
The HR diagram has many forms. There is no one to one relationship between temperature, colour and spectral type that is true for stars of all surface gravities and metallicities.
Spectral type depends on temperature primarily but spectral features can also be weaker or stronger at lower surface gravity or with changes in metallicity.
For example, the Handbook of Space Astronomy and Astrophysics has two tables of spectral type Vs temperature relationships, one for dwarfs and one for giants. And indeed the M-type giants are cooler than M-type dwarfs of the same subclass by ~200K.