Based on Mozilla's documentation, it looks like CHIPS only applies to "cross site" cookies that are just accessible on different subdomains of the same site. A third party cookie could share data between a.site.example and b.site.example if it asked nicely, but not on site2.example.

If this isn't about it subdomains exclusively, it's not apparent to me. But it's all pretty confusing, and CHIPS appears to be just one minor thing that Google introduced when they were creating Privacy Sandbox back in 2022. (You know, to facilitate the total removal of third-party cookies, something they eventually backtracked on anyway.)