The stitch consists of two back to back lines of blanket stitch whipped together with another thread. I like the blanket stitch so I enjoyed stitching this example.
I filled in another of the boxes on my sampler again using variegated silk thread and then outlined the box using the same thread and stem stitch.
|Blanket stitch is worked with the needle away from you.|
The thread passes behind the needle but no knot is formed.
|Buttonhole stitch is worked with the needle towards you.|
The thread passes round the tip of the needle to form a knot.
|Buttonhole stitch.... can you see the knot?|
You can read a post I wrote explaining what I think the difference is here. I am only self-taught, so this is really only my own opinion but, in that opinion, there is definitely a difference in the stitches but, you judge for yourselves.