Despite being advertised as a new game or "stand alone expansion", Rising Storm is more or less an enhanced version of Red Orchestra 2 with the Pacific Theater added. It adds the American and Imperial Japan factions, a new armament of weapons and 4 new maps: Saipan, Betio, Hanto, and Iwo Jima. It also scraps the Single Player mode. Playing Rising Storm/Pacific Theater content is as simple as joining a server hosting it (both games share the same server browser); they will have the letters RS at the beginning of the map name.
Rising Storm includes all of Red Orchestra 2's content and is available free for owners of the original RO2 who purchased it after September 2014 (in fact it's included in all the latest updates so you don't really have a choice). If you purchased it before September 2014 you can pay a small upgrade fee to unlock all the Rising Storm content, otherwise you can only play as a rifleman. As of 2018, Red Orchestra 2 and Rising Storm still have separate Steam pages despite providing the same game and content.