Of course, I dare say it's just my description rather than the correct terminology.
I'm talking about when you measure out a strip of crosswise lycra (same fabric as the body) around 85% of the neckline length plus seam allowances, then sew the ends together to make a loop. Mark both the loop and neckline in quarters (or eighths if it's quite a long one), sew it together then fold over and under and machine down. This
Jalie video shows it well from 1:34mins in. They sew in on the wrong side and fold it outwards giving an effect that looks most like that done with a binder attachment. I like that for stretch mesh (as it is in the video) but for ordinary lycra I prefer to sew it to the right side then fold it over, not always bothering to fold the cut edge under. I often just top stitch it with my coverstitch and trim off any excess.
With regard to the facing, if you sew the band to the right side then turn it over until the strip is folded entirely to the inside hiding the lycra loop from view, it effectively becomes a facing but a very narrow one. Here's a video from
Professor Pincushion.