Since BSW and BSF are not A/F sizes, I suspect that they were originally Anglicised (Imperial) metric sizes,
No, or VERY few, hexagon sizes are going to be exact because of tolerances (Not all 1/2 A/F or 13mm hexagons will be the stated size; a spanner that is a snug fit on one nominal size might well be a slightly loose fit on the same nominal hexagon from another source).
Hopefully, asjustable will have jaws that are not so slack that they slip and damage the fitting.
Things like Stilsons, Footprints, and the like, have teeth, specifically to grip. They do but leave marks; which are not always acceptable except in “nothing to lose” situations.
Howard