Both works deal with the same time period and individual. El Cid was a real person living in eleventh century Spain.
However, Fletcher's The Quest for El Cid is a historical document that focuses on a historical era. El Cid is merely a vehicle to narrate that history. Fletcher recognizes that El Cid is largely a poetic figure who became popular through medieval epics like The Poem of El Cid. Fletcher tells the historic account of the individual who would later come to be known as El Cid.
The Poem of El Cid alters many of the facts of that individual. For one, the poem describes El Cid as a hero who is Christian, loyal to the king, and a devoted Castilian. The real Cid, Rodrigo Diaz, was exiled from Castile following a disagreement with the king and lived for many years in Zaragoza, working as a mercenary for a Muslim ruler. He would eventually defeat the king in a battle for control of Valencia.
The Poem of El Cid attempts to turn the historic figure into an epic hero, embellishing events to emphasize the man's generosity and devotion to the king. In real life, Rodrigo Diaz was an ambitious individual who sought to gain power and territory for himself.