Hangul has order because it's enumerable. Hanja on the other hand, does not have order and it's not enumerable.

(not enumerable as in written text as strokes can be combined and invented on the fly, enumerable if you think it's a finite charset on computers)

New characters can be invented on the fly, but not every random scribble would be considered a character. In practice, only a handful of different stroke types are used, which gives even newly invented nonsense characters a recognizable visual style. For any finite stroke count, there's only a finite number of combinations, so the infinte set of characters with unbounded stroke count can be enumerated.

It can also be sorted using the radical and stroke count, although then you can't enumerate it in order because there's an infinite number of possible characters for each radical.

It's so annoying how "CJK" groups Hangul with completely different writing systems. And even makes people think they're similar.

Well, Hanja can also appear inline in otherwise Hangul texts. Vietnamese has a similar issue though their use of an extended Roman alphabet ended up in a slightly different place, Unicode-wise. I don't remember the decision but I believe it might have been at the request of some RoK people.

There might also be an issue if old Hanja-only texts need to be handled differently from Hanzi rendering/processing. That would not surprise me.

Still, I agree it seems pretty weird.

Hangul and Hiragana are not so dissimilar AFAIK? But the point of saying "CJK" is the other direction: codepoints subject to Han unification may represent Hanzi, Kanji or Hanja.

Hangul is actually just an alphabet. Each square hangul character is composed of 2-3 letters. Hiragana is a syllabary.

> Korean alphabet (Hangul) is fully ordered

Buuuut historically, there have been several ways to arrange Hangul linearly, and the prevailing sorting in dictionaries differes between North and South Korea.

This is why I had to point out that order does exist, just that there are too many such orders.