start_remote_hdp_services are the services which you installed on other nodes. For example if you have services installed on Node1 2 and 3. If you run start_local_hdp_services on Node1 then the services installed on Node1 will start. If you run start_remote_hdp_services then the services on Node 2 and 3 will start.
This is dependent on the configuration of the cluster and configuration of the batch file.
It is not a HDP ‘mode’ as such.