Yes, there is a difference between the THREE designs.
The single pot with two holes in the side to define the upper limit of the reservoir is pretty much "self flushing". Every time you water, you fill the pot rapidly to the top with dilute fertilizer solution. That 1) flushes, and 2) saturates the medium, and 3) refreshes the chemistry of the reservoir.
The 3-component setups (Leni or Luwassa are common trade names), consisting of a mesh inner pot containing the LECA and the plant, an outer pot to create the reservoir, and a gauge to help control the reservoir depth, works similarly from a water-delivery to the plant perspective, but requires removing the inner pot from the outer pot, dumping the old liquid, separately flushing the medium, then reassembly before refilling the reservoir.
The two problems with that design, in my mind, are the ability to overfill the outer pot, drowning the roots, and the hassle of proper watering tends to "lull" people into just topping-up the reservoir without flushing, accelerating the buildup of minerals and wastes.
The "self watering pot" you linked to, similar to just using a container with no drainage holes whatsoever, provides no convenient way to flush the medium, again, leading the grower to just topping-up the reservoir.