"Page" is clearly too ambiguous as almost any acronym will be. The main tenet of a Single Page Application at least used to be, before it was buzzworded into ambiguity, that the browser loads everything it needs once and makes round trips only for new data or incremental functionality. I think the same definition is still applicable, though. It never had anything to do with the information architecture of your UI or whether the majority of the screen might change between pages. And nothing to do with the URL or history; that's all orthogonal and now can and should be done with deep linking and the history API to allow people to have faster feedback and still interact with sites in the browser the way they always have.

Single page load is the definition. The page never reloads. Even the first SPAs would uses url hashes to change the url before pushState was adopted.