Not a technically different page, specifically different content. Serving different pages to Google is fine, as long as they contain the same primary content that the real pages do. That's the whole point - so you can serve prerendered pages to Google but still have a JS-based frontend for the actual users.
AJAX sites often lazy load in content later. My point is the page delivered initially is not the same as the static version content wise or technically.
This is exactly correct. Regardless of your motivations.