Hi I'm from a Blender background. I have only known vertices, edges and faces.
Here there are primitives, polygons and points,vertices.

How are they different ?

Primitives are objects which are recognized by Houdini as a single entity. For example a sphere that isn't made up of points and faces but is mathematically defined as a single shape. With the new PolySoup tools in H12.5 you can turn a complex piece of geometry into a single primitive which offers a number of efficiencies. Alembic files can also be brought in as primitives for more efficient handling.

Our Polygons are faces in blender.

Our points combine vertices from different polygons that share the same point in space. It is possible to break these points into multiple points using the facet sop or to fuse different points into a single point.

Vertices are polygon specific. So the corner of a box would have three verticals and one point. The vertex sop lets you mange these separate from points.

You can now cusp the normals of a model to affect the smoothing of the edges. In the past we would need to use the face sop to break up the points.

Thank you for the very clear explanation rmagee