RA-RNTI and C-RNTI both are different, RA-RNTI is calculated based on t_id and f_id while T-CRNTI is allocated by eNodeB MAC to UE so that once connection is successfully established between UE and eNodeB this T-CRNTI is used as C-RNTI to identify the UE at eNodeB MAC layer .
Formula to get the "RA-RNTI = 1 + t_id + 10 * f_id". In case of FDD cell, value of f_id is zero where 0 <= t_id < 9.
In short, RA-RNTI is generated at the UE while T-CRNTI is at the eNodeB.
Hope I answered your query.