Short version: The Hario brand filters are thinner than other paper filters and seem to have more texture than other types of filters. I assume this has some, but perhaps slight, impact on the rate at which water passes through the filter and also what "stuff" passes through the filter, which impacts the resulting brew and its taste.
Longer version: The rest of this response is basically a comparison of the Hario filters to other types of filters. This isn't particularly authoritative nor scientific. I don't immediately find any good online resources on this; one video that I don't care to link or watch, and another article from Serious Eats on dripper styles but it doesn't compare the filters themselves as such. So, I'm going rogue.
The different cone (and filter) manufacturers each have their own shape, presumably to ensure product lock-in for consumables (in this case, primarily filters). Here are the three primary ones that I'm aware of:
Clockwise from upper left: off-brand Melitta-style #2, Hario brand V60 02, Chemex brand pre-folded bonded. All are "natural" brown (unbleached, etc.) varieties.
My basic summary, having looked at these three examples from my own stockpile (certainly, this is a small sample) in order from thickest to thinnest:
- The Chemex filter is very thick; almost more like like a thin pressed cotton cloth or fabric. Almost completely opaque. The Chemex filter page states that they are "20-30% heavier" than other filters and removes finer sediment and "undesirable oils and fats".
- The Melitta-style is in the middle, and is similar in nature to most other Melitta-style and basket-style filter paper. Thick enough to be mostly opaque, but noticeably thinner than Chemex. The Melitta brand filters have claimed "flavor enhancing perforations."
- The Hario brand is the thinnest by a fair margin. It's almost translucent through most of the filter, with a somewhat leaf-vein-like pattern to it, presumably from paper fibre and production method. This brown ("natural") style seems to be called "Misarashi" for reasons I don't understand. There's little information on the Hario (.co.uk / .jp) pages about the nature of the filters.
Frankly, I don't notice a significant difference in coffee draining rate (throughput), but I suspect there is. I (personally) think there's a slight difference in taste and output of the brew, but perhaps I'm fooling myself into legitimizing more coffee gear.
As stated in this other question about Hario V60 filters off-brand filters do not seem common (in our regions).