In the WSAPI page under Object Model we see objects named: "PortoflioItem" , "PortfolioItem/Feature" and "PortfolioItem/Initiative". What is the difference between these endpoints?
The portfolio hierarchy is defined per workspace. It is dynamically set by a workspace administartor.
The PortfolioItem endpoint is a parent to any and all portfolio item hierarchy items. Let's examine an example.
In this example your workspace has the following hierarchy for portfolio items:
For such a workspace, Rally will dynamically generate 3 new endpoints called: "PortfolioItem/Theme" , "PortfolioItem/Initiative" and "PortfolioItem/Feature". All these endpoints will share a common parent endpoint called: "PortfolioItem".
What this essentially means is that the common fields between your portfolio hierarchy levels is defined on the parent - on the PortfolioItem endpoint, while specific functionality or behavior can be defined on any particular level.
Furthermore, the dynamically generated endpoints for the three levels will include a full REST interface for Create,Update,Read and Delete which you can utilize by http.
You can also read more here, on the relationship of the portfolio hierarchy and user story hierarchies.
For more on portfolio items relationship to user stories - see here.