Both your statements are true :
EXIF data may contain an embedded thumbnail generated by the camera, depending on the camera model.
Some image editors may embed a thumbnail in image files of a format that can contain one, such as JPEG. TIFF encoded files often embed a JPEG image as a thumbnail of the main image. Even MP3 files can contain a JPEG of cover art, in the ID3v2 tag.
However, thumbnails created by image editors are never stored in the EXIF data, as that part is normally left unchanged by image editors, since it taken as belonging to the camera and not to the image. Also, this is usually not done automatically, but requires some user-action.