In all honesty I don't know enough about 'backsword' or 'shortsword' systems to have even a vague clue on any techniques, so I'm just going on what I've seen on youtube etc. From this it seems that the systems don't work from the bind, ie the 'pull off' and strike to another target.
When consdered against the rapier, of which I've studied a little, this is a significant difference where many actions work from the bind and even include 'winding' in a loose sense.
So perhaps the term is used to differenciate between weapons that are used in different ways.
With my interpretation of Ledall the terms 'forwards' and 'backwards' relate to the direction in which the blade travels once blades have bound ('crossed' in the English). In other words a blade that maintains the bind and works 'behind' the opponents blade, as we would say in modern terminology, moves 'forwards'. While a blade that 'pulls off' and strikes elsewhere moves 'backwards', away from your oppentent. Systems that use the backsword seem to have little use of the back edge, and with the development of the basket meaning you can only hold the sword one way, means they loose the second edge, the new style of weapon taking the name of the system that primerily moves 'backwards'.
God, righting this on a phone isn't easy!