The most important job of VACUUM is usually to make sure that queries remain responsive -- it's roughly comparable to a "full scan" within generational garbage collectors (for managed language runtimes). VACUUM does reclaim space in various ways, but that's often considered to be of secondary importance.

In Postgres, the on-disk representation is virtually the same thing as the in-memory representation used by pages stored in the buffer cache. In a system like Aurora or Neon, the representation of pages in the buffer cache is identical to that of Postgres (or has very minimal divergence to deal with one or two isolated problems). That part doesn't really change, which makes it possible to have a very deep level of compatibility without much effort. So it's radically different in one narrow, scoped way, but otherwise very similar.

While the storage knows how to materialize pages on demand, these are not transactionally consistent pages -- they often need to be interpreted by using metadata about transaction commit status, just like in Postgres.