I am learning about postgresql internals and I am wondering or postgresql B-tree index is actually classic B-tree or B+tree? To spell it out, that means the nodes contain only keys or key-value pairs?
I said B-trees, first, but it's arguably closer to B+ trees.
See iwis' answer discussing it more thoroughly.
You would really have to consider index + heap (+ auxiliary storage) together. An index is mostly useless on its own.
Here is a related chapter on Wikipedia.
The name of the relevant index method is "B-tree" in Postgres. Physical storage is very similar to that of tables (the heap) or any other index type. All use the same data pages with mostly the same page-layout. More in the manual.
Development is ongoing. The design has been changed (improved) in many aspects since this question was asked. The latest notable change (as of April 2021) being deduplication in Postgres 13.