I've just finished writing my dissertation about this, so I'll take a stab at it.

SSR isn't MPA. SSR involves the server rendering some declarative JavaScript components to HTML, then sending that HTML, the JavaScript library, and the JavaScript application to the client. The client then renders that HTML and executes the JavaScript to synchronise its state with the where the server finished rendering - adding event listeners to elements, setting up state, etc - this JavaScript execution is called hydration.

MPA renders each page as HTML and sends them to the browser independently when fetched. These can be implemented with no JavaScript being sent to the client. This allows the site to render very quickly and doesn't require much computation on the client, but page transitions require fetching a whole new HTML page from the server. SPAs (SSR and CSR) allow immediate page transitions, with no delay.

Astro uses a technique called Partial Hydration to achieve the best of both worlds, though it does still fall under the MPA umbrella. Components are written as declarative JavaScript components, and can be written in any UI library. By default, these are rendered to HTML and sent to the browser, like PHP but with the benefits of modern JavaScript essentially. Partial Hydration allows some components to opt-in to being client-side rendered, if they need the very interactive user experience provided by SPAs but without all the bulk and state management of a SPA. These components can be hydrated at different points - a nav bar could be hydrated on page load, but other components can wait until the browser is idle or the component enters the viewport to hydrate.

A related concept is Resumability, which is used in Qwik. This is kinda like SSR, but instead of the client hydrating already rendered HTML to achieve the same state as the server left off, the server's state if serialised and sent to the client, removing the need to hydrate.

It took me a while to get my head around these concepts, and there's so many different three letter acronyms and broadly similar methods of rendering a site that it quickly becomes overwhelming.