KWrite uses the Kate editor KPart, Kate obviously as well
KDevelop uses the editor component which is configured in control center, by default this is also Kate part
The difference between KDevelop and the other two is pretty clear: it is an IDE the other two are editors.
KWrite is aims at providing a simple text editor, while Kate provides a more complex GUI for working with lots of files, for example for developers that do not want to use an IDE.
Kedit is an addon editor (kdeutils if I remember correctly) and provides support for languages written right to left
Cheers,
_