[OskarS]

I grew up with Swedish crosswords, where the clues are written into the "non-letter" cells (the ones that are shaded in an American crossword). There's no separate clue section, it's just all part of the grid. They almost always have some illustration as well, they look really delightful compared to American crosswords, though from a "puzzle" angle they're not always as fun.

[NeoTar]

I think that might be called an 'Arrow word' in at least some English dialects, if I am getting your description correct in my head...

E.g. see: https://images.app.goo.gl/mErh6pEEnR9Eexpf8

[OskarS]

Yes, that kind of thing, but with an illustration and usually styled nicer. This is a very typical look (the first crossword i found by googling): https://www.argument.se/wp-content/uploads/2018/10/Korsord-2...

[eb0la]

In Spain they're called Autodefinidos: https://es.wikipedia.org/wiki/Autodefinido