Taking a look at the comparison paper [0] provided on that site, there does seem to be a significant difference. The images generated with MS are more prone to long horizontal lines while WFC produces larger blocks of texture. This is hard to spot with more homogeneous textures like pipes, but it's more apparent with something like the grey cat faces, where WFC generates a variety of shapes and MS mostly makes very long ones. Going back up to section 2 I found the explanation: "Model synthesis sweeps through the grid in scanline order. WFC chooses the lowest entropy cell." The results from WFC look more natural and varied to me so I'd call this a significant advance.

But it does seem appropriate to say they're variations of the same algorithm. As for the name, I don't like either: Wave Function Collapse is based on a silly pop-science interpretation of quantum mechanics, and Model Synthesis is extremely generic and forgettable. And it's not even a synthesis, more of a filtering process. I guess I'd stick with Wave Function Collapse.

[0] https://paulmerrell.org/wp-content/uploads/2021/07/compariso...