Reactive arthritis is arthritis caused by infectious agent & it includes Reiter Syndrome so Reiter is part of Reactive arthritis.
We say Reiter Syndrome when we have arthritis+conjunctivitis+urethritis
Why Have Some Forms of Reactive Arthritis Been Called Reiter's Syndrome?
One could also ask, "Why isn't Reiter's syndrome called Reiter's syndrome anymore?" The answer is that the syndrome, or group of symptoms, is named for Hans Reiter who described a soldier with the triad of urethritis (burning and pain with urination), conjunctivitis (redness and pain of the eye) , and arthritis (swelling and pain of the joints) after having bloody diarrhea in 1916. However, the history of this constellation of signs actually predates his description. And what is disturbing is that Reiter was a high-ranking Nazi official who was responsible for medical experiments in concentration camps (Panush, et al., 2003 and Petersel & Sigal, 2005). As a result, the term Reiter's syndrome has fallen out of favor and Reactive Arthritis is preferred to describe the post-infectious arthritis which may be accompanied by extra-articular manifestations (such as urethritis and conjunctivitis)