These values indicate the current state of the checkpointing lifecycle. In particular CONTINUE/RESTART are set by the checkpointer in the CRS (all others are used by the INC mechanism). In the opal_crs.checkpoint() call the checkpointer will capture the program state and it is possible to emerge from this function in one of two scenarios. Either we are continuing execution in the original process (Continue state), or we are resuming execution from a checkpointed state (Restart state).
So if the checkpoint was successful, and you are not restarting the process then you want OPAL_CRS_CONTINUE.
If the process is being restarted from a checkpoint file, then we should emerge from this function setting the state to OPAL_CRS_RESTART.
The OPAL_CR_CHECKPOINT state is used in the INC mechanism to notify all of the components to prepare for checkpoint (we probably should have called it OPAL_CR_PREPARE_FOR_CKPT). So not really used by the CRS mechanisms at all. You can see it used in the opal_cr_inc_core_prep() function in opal/runtime/opal_cr.c