However, any other action with the process instance is done by using processInstance as entry point, e.g. in order to get the details of an instance one needs to issue an GET to
/processInstance/{processInstanceId}
Is there a specific reason for the different entry points?
There is no specific reason for that, probably an oversight with has been there from the beginning… To ensure backwards-compatibility, this will be kept I guess. However, feel free to add a Jira which describes this, it's always possible to add additional URL-mapping for the rest-resource to be consistent.