If we want to honor the D&D tradition of splitting hairs of various infernal creatures:

The difference between demons (such as succubi) and devils is the conflict between Chaos and Law. Since newer editions are bad at explaining this, let's harken back to old times:

The chief conflict between Chaos and Law is that of the individual versus large, organized groups. Hence, when it comes to extremely Chaotic Evil creatures such a demons, even the lowliest them of thinks of itself as the center of the universe - and any suggestion otherwise is offensive to them in a way that makes them want to hurt somebody. They won't really obey anyone unless it pleases them personally or somebody's forcing them.

Lawful Evil creatures, such as devils, don't think like this. They believe there is a hierarchy to the world, with the Better People deserving to be on top and the Inferior People on the bottom. As corollary, lower-level devils don't need a reason to obey the usurper king other than that he's on their side - he's the Chosen One who will bring Hell on Earth for greater glory of Devilkind. They will happily bend the knee to their king it means the rest of creation will be made to bend the knee before them.