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Forgot to add that the mirror world(s) are accessed by the riders from Ryuki through any reflective surfaces, not only mirrors.

It is called the mirror world, but they do differ from mirror dimension. What you say about the mirror dimension is correct, I think. As for the mirror world, it’s meant to be a world that is ‘mirrored’ from the real world. From the novel, the mirror world has its own time and space disconnected from the real world. And, fun fact, there are countless mirror worlds. Side note: Worlds here actually means universes funnily enough. The novel gave an example where if you put two mirrors facing each other, they would make countless reflections, and the mirror world basically follow that logic. Hence, the mirror world is basically parallel universes that are mirrored to the real world and each other, but each iterations of mirror worlds will be slightly different from the preceding iteration. The novel actually explained that this is how the winner’s wish is granted in the series, by giving them a world/universe from the countless mirror worlds that basically fits with the winner’s desire and place them there. (Not so fun fact: This is also why the rider wars in Kamen Rider Ryuki can’t really end because there are essentially countless of them happening across different worlds through the mirror worlds.) Most of the in fact are from the novel if I’m not mistaken.

Well, the mirror world from kamen rider Ryuki works quite differently enough from the mirror Dimension that it’s reasonable enough that they’re different. Only the names are similar and they don’t work the same.