Apple News is really just RSS. I think Gruber's Daring Fireball stuff in Apple News just comes from his RSS feed. It's all hosted on your servers, so it's basically just a specialized browser.
AMP pages don't intrinsically live on google.com. Rather, when you use Google Search on mobile, some results may have AMP equivalents, they're often prioritized on or closer to the top [1] or otherwise highlighted (like in a carousel). As of writing, these results are marked with the lightningbolt-in-circle logo and the text 'AMP' somewhere in the result's most immediate box [2].
Clicking on one of these AMP results in Google Search will lead to a Google-hosted page with the base URL of "google.com/amp/", which loads an iframe (or equivalent) of the AMP article content. This whole thing takes up the entire viewport, save for a small grey horizontal bar up top, which collapses (hides) with JS if you scroll down far enough, but is otherwise pinned to the top, staying adjacent to the browser chrome.
This AMP navbar, as of time of writing, has the original publisher's domain name in the middle (which isn't a link, just informational text); then on the right side is a link ("chain-link") icon which will produce a small overlay containing the article's original (non-AMP, non-google.com/amp/ link), and a vertical triple-dot button with a link to 'More info'. This 'More info' link takes you to a Google Search Help article [3] (along with a really, really long visit_id as a tracking parameter), which talks about AMP and the Google AMP Cache, says that "The Viewer is a hybrid environment where Google and the third-party webmaster may each collect data about you", links to a few FAQs and the Google privacy policy, and the like. In the past, the navbar was different [4], and its deficiencies where a frequent source of criticism.
In short, Google Search on Mobile serves AMP results out of Google's own AMP Cache in a not-completely-obvious in-place wrapping viewer that tracks your visits, but it's now possible to get original URL [4]. Meanwhile, Cloudflare, currently the only other operator of an AMP cache, offers auto-AMP links [5] for customer domains, and offers an SDK to customize the wrapper-viewer [6] that will surround the articles surfaced for that domain.
Apple News is a client application that combines a feed-reader with articles delivered from Apple News' servers; these latter types of articles are always hosted by Apple [7], and in the beginning the only way to publish to it was to use Apple's APIs to post to Apple News directly [8][9]. Now there's integrations that will consume content out of your CMS and post it to Apple News on your behalf, which makes it easier to use, but doesn't change the fact that the the content is published into Apple's ecosystem.
