If you cast summon greater demon, it says
You utter foul words, summoning one demon from the chaos of the Abyss. You choose the demon’s type, which must be one of challenge rating 5 or lower, such as a shadow demon or a barlgura. The demon appears in an unoccupied space you can see within range, and the demon disappears when it drops to 0 hit points or when the spell ends.
It says demon, but what creatures qualify? Clearly, it’s not all fiends, because devils are different, but it can’t just be creatures under the demon section of the monster manual.