You are right. Sorry. I saw them as equivalent in other posts and I quoted the wrong one.
Happens to be that their are possible shitos in each sugya that would make the fraud to avoid paying more likely to be asur than the fraud to gain money.
Also, as far as the question of whether it's actual gneiva/gzeila or some other issur, the Shulchan Aruch Harav quoted above says it's actual gezel (ADG's pathetic attempt at being midayek in his lashon notwithstanding).