Everyone who has enough background to provide the OP with valid information about the distinction between RAW and JPEG files is aware the Nikon DSLR's that you own embed a full sized JPEG in every RAW file.
In fact Nikon embeds three JPEG images into every NEF file. There is a full sized JPEG and a smaller one in the Exif data. The thumbnail that you mentioned is actually in the MakerNotes.
In fact there is one more JPEG image, embedded as a "comment" in one of the others. I don't recall, but it is probably embedded in the preview image, and is a very small preview image used when multiple images are show in a list on the camera's LCD screen.
You can use any good tool that extracts Exif data to find them. I'd recommend Phil Harvey's exiftool, which is free.
Here is the way to extract them:
>exiftool -previewimage -b dsc_xxxx.nef > previewimage.jpg
Change "previewimage" to "jpgfromraw" for the full sized JPEG, to "otherimage" for the small JPEG version. Using "previewimage" produces a 570x375 pixel thumbnail.