that second combination is less well known, but it really is the same thing. the caching plugins generate and store the final html for each page, including the front page, lazily or eagerly, and serve it straight from disk without running *any* PHP. when someone posts a comment, or you update a page, or anything else that matters changes, the caching plugin wipes the stored html. it all works really really well.
totally! there are obviously a number of established examples of this. a couple of the most relevant are jekyll + disqus (or [webmention.herokuapp.com](https://webmention.herokuapp.com/), etc.) and wordpress + wp super cache or total cache (plugins).