The Equal-i-zer is made by Progress Mfg, not "Progressive Industries." Close, though! I have one, and used it in the past with a 23' Rockwood. The bars are forced up onto L shaped brackets attached to the trailer's frame. The friction between the bars and brackets, plus the friction in the head sockets the bars fit into at the front end, dampen sway and keep it from turning into uncontrolled oscillation.
The photo you showed us, Cathy, looks to me like a run of the mill, budget priced weight
distribution hitch. It does not provide a significant amount of sway control. A friction bar or two could be added to the setup for sway control, but they aren't IMO as effective as the Equal-i-zer brand, the Reese Dual Cam, or the Anderson.
The Anderson No-Sway is quite new. Hasn't been out more than a year or so. Their website shows how it works much better than I could describe it. If there is a weakness to their system, it might be the way the chains when tightened draw the trailer coupler forward against the ball; a couple of people have observed damage to their coupler pawl after a while, and they spoke of plans to replace their coupler with another brand (like Bulldog) that grips the ball differently.
Cathy, if your rv dealer is telling you that this hitch is 'just like an Equal-i-zer" or "just as good" as one, remember the old adage on how to tell if a salesman is lying to you: are his lips moving?