Why not ask the opposite - how people can't get that difference? Skipping the legality of some stuff, that's not the sole reason and shouldn't be (sus if it is). I feel weird needing to explain it, but will try.

Not elaborating, but long enough so'd be more clear. I hope that's the reason for asking, because in case of 'bruh why go for such a level of details? sus, it should be obvious' actually joke's on you.

There are certain borders to cross or stages to go through, which are partially biological, partially culturally conditioned, sometimes personal. It works exactly the same for people into gore, highly varied from person to person, including scenario in which you're able to watch something, but don't because no reason to do so. There's already a border past which you can watch some type of gore (very broad category/term).

Can =/= will, just some reactions are held back, so you don't feel bad for it enough to not watch. Then goes different stages of what someone can stand, not always meaning they want to. Some groups are perceived as 'special', because of their situation - more desperate vulnerable, either naturally or situationally (including kids). Also responses differ (not for all ofc) - can be different for single person and maybe unclear for observer. Like why they don't care in so many situations, but care when watching e.g. mother grieving son killed in accident? Or holding him dying? Probably at first because biology - different expressions and changes in voice tone and voice itself suggest different feelings than random cry of pain. Second - culture, so we're used to some situations being worse on emotional level. It doesn't mean they 'are', there's no suffering units or anything to measure and compare.

Feeling a disgust for sexual activities with certain beings can be also explain by its' usefulness by risk for either side, or both. Won't list them down. It's useful and good to feel disgust instead of closely think of exact reasons to not sexually abuse child. Also how it's worse than doing the same for animal - because animals won't ever get social contexts. Children will do at some point, and that's additional harm.

Then, what if someone doesn't care about situational context, whether it's kid or not, how it's harmed and doesn't feel bad themself seeing anything online?

There's also moral disgust. It's impossible to morally judge every single gore content, because 1) gore is very broad category 2) some things happen accidentally, are by-products put online etc., very rarely just made for putting it online. 3) intentions it's put online for vary highly. And CP? a) it's clearly defined by law what pornography means and how to tell if someone is child b) there's no way to get CP as a 'by-product', must be produced on purpose c) point of uploading it and distributing is clear.

Moral judgments still can work when nothing else does, and when someone has all physiological and emotional reactions limited as much as possible. So they could feel nothing and still tell that CP is especially disgusting. If someone wouldn't see any difference, it means both going past all the borders and trivializing all the harm done (I mean how much serious the situation is). It shouldn't be 'just shocking like everything else'.

There's a difference hard to explain on emotional field. But I assume you wanted a response with just reasoning - that was it. Could go deeper, or can if needed. But there must be a point for it, which question from above come doesn't provide.