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The GraphHopper Directions API is a collection of routing related APIs: like the Routing API, the Matrix API, the Route Optimization API and the Geocoding API. See here for a more detailed comparison.
For example: the Route Optimization API is an efficient way to consume jsprit: properly configured for a lot of use cases, with a proper distance/time matrix calculated from the routing engine under the hood, with a simple JSON API and some advanced features not in jsprit.