How is the last part any different? The server still renders HTML with a JS block requesting your view data (via JSON) and then the JS code (using Angular) renders it.
This means, among other things, you don't need server-side URL routing or templates. (You need routing for the REST layer, but that can usually be dynamically generated.)
It's just a much stricter separation: the client deals with view logic and HTML and all that, the server deals with pure business logic behind defined interfaces and data formats.