Detached Buttonhole Stitch vs Brussels Stitch

In a couple of books I have where I’d expect Detached Buttonhole Stitch to be used, Brussels Stitch is used instead for the same purposes.
These include :

• The Barbara and Roy Hirst Raised Embroidery/Stumpwork books
• Elizabethan Needlework Accessories by Sheila Marshall

I wrote to the Historical Needleworkers List and asked why this may be.
The answers (quoted with permission) were :
“I have always thought that the Brussels (Bruxelles) Stitch, the Detached Buttonhole Stitch, and the Venetian Cloth stitch were basically the same stitch, just invented or used in different situations.
Getting from one row to the next is different in Brussels stitch than Detached Buttonhole, because one is doing different things. But my understanding is that the stitches are basically the same stitch.
I would expect that one would identify the stitch as one or the other based on where one had first encountered it. 
That is, if one did needlelace before coming to Elizabethan raised work, one would continue to call that stitch a Brussels stitch.  So I don't think it strange at all that Sheila Marshall's book identifies it as Brussels Stitch - I bet she has done needlelace.
I suspect that the same stitches have been reinvented many times, for many situations, and that is how stitches get multiple names.”
- Baroness Eowyn Amberdrake
Another answer I got was
“Brussels stitch is a needle lace stitch. The method of working is similar to button hole stitch except in Brussels it is upside down. Instead of the needle coming out at the top through a loop, it comes out the bottom through a loop and those loops are built upon in successive rows in pattern.”
- JoEllen/HighlyUnlikely (that’s her net name, not a comment)
Brussel Stitch also comes Corded (with a Return thread), Double and Treble (ref New Designs in Raised Embroidery, Hirst)


(the second image being Detached Buttonhole Stitch, from Jane Nicholas’ Complete Book of Stumpwork Embroidery”.
The first image is from New Designs in Raised Embroidery by the Hirsts.
Note that with the Brussels Stitch, the thread is wrapped around the outline, rather than the outline being pierced through the ground as is done with Detached Buttonhole Stitch.