In any given situation, if there is no standard (and even if there is), it is good practice to define your terms accurately and unambiguously at the beginning. We've certainly done that here. The first thing I see when I open the link you reference is a definition of what they are calling "angle". I fail to see the confusion here: they are referring to half the "razor angle".

When we tell someone that they should put a 20 degree angle on a knife, we mean that they should sharpen each side to 20 degrees. This creates a total angle of 40 degrees. So when we’re talking about the angle on your knife, we’re talking about the angle at which you hold the knife to your stone.
Does your "Lansky" system define what it means by angle? Perhaps that is where the confusion sits, because AFAICT that link you posted is very clear.

James.