So you have these debates over here as well, do you? I can set my calendar by how often one will start at AG.
I don't actually think I've ever seen a proper definition of "casual". I've seen lots of generalized descriptions, but none that really capture the
defining characteristics. Most people have two eyes, two ears, and a nose, but it's not actually a requirement to be a human being. When I hear people say a casual game can't be an adventure because it's too easy, too streamlined, too lightweight, Randy Newman's satirical "Short People" tends to pop into my head.
Of course there are differences between casual games and full-length adventures, but that doesn't mean they're unrelated. There's a big difference between a Big Mac and a sit-down steak dinner, but both are perfectly legit meals. They just suit different needs and particular tastes at any given time. And really, casual adventures are just the genre's version of fast food.
Ultimately, I think comparing "casual" and "adventure" is misleading, as they aren't inherently conflicting terms. To use another analogy, it's like comparing television and movies. Certainly those seem like very different things on the surface, but you can WATCH movies on television, and there are even made-for-TV movies. So yes, sometimes they are very different, sometimes fully compatible. Context matters.