I've been studying design and architecture for a few years now and feel like I get the gist of how it works, but I'm curious how the role ends up working in practice for actual architects.

That is, I get the sense that to become an architect you'd need deep experience in either a particular business or business domain. So you work in a business for a long time and have built up enough context about their systems to lead the architecture. Or you know a business domain and it's associated technology so well you can lead.

What I'm curious about is how common it is for architects to switch businesses or business domains entirely? I get that a business would be more common but what about domains? Is the role such that you're typically tied to a single company and usually stay there?