The New World

In 1607, Pocahontas, the spirited and adventurous daughter of Chief Powhatan, and others from her tribe witness the arrival of three ships sent by English royal charter to found a colony in the New World. Aboard one of the ships is Captain John Smith, below decks, in chains. While initially sentenced to death by hanging for his mutinous remarks, once ashore, Smith is pardoned by Captain Christopher Newport, the leader of the expedition.
While the prospects for the settlement are initially bright, disease, poor discipline, supply shortages, and tensions with the local Native Americans (whom Newport calls "the naturals") place the expedition in jeopardy. Smith takes a small group of men up river to seek trade while Newport returns to England for supplies. While on this mission, Smith is captured by a group of Native Americans and brought before their Chief Powhatan. After being questioned, the captain is nearly executed. He is spared when Pocahontas intervenes and saves his life.
Living among the Native Americans as a prisoner for an extended period, Smith is treated well and earns the friendship and respect of the tribe. Coming to admire this new way of life, he falls deeply in love with Pocahontas. She is intrigued by the Englishman and his ways. The chief returns Smith to Jamestown with the understanding that the English are to leave the following spring, once their boats have returned. Upon his return, Smith encounters the settlement in turmoil. Pressed into accepting the governorship, he finds the peace he had with the Natives replaced by privation, death, and the difficult responsibilities of his new position. Smith wishes to return to his love but dismisses such action. He thinks of his time among the Native Americans as "a dream" from which he has awoken. Their numbers dwindle throughout the brutal winter, and the settlers are saved only when Pocahontas and a rescue party arrive with food, clothing, and supplies.
As spring arrives, Powhatan realizes that the English do not intend to leave. Discovering his daughter's actions, he orders an attack on Jamestown and exiles Pocahontas. Repulsing the attack, the settlers learn of Pocahontas' banishment from her own homeland. They organize a trade so that the young woman can be taken captive and used as leverage to avoid further assaults. Samuel Argall convinces the settlers on a trading expedition up the Potomac River to abduct Pocahontas from the Patawomecks as a prisoner to negotiate with her father for an exchange for some captive settlers, but not the stolen weapons and tools. When Smith opposes the plan, he is removed as governor. After Pocahontas is brought to Jamestown, she and Smith renew their love affair. The return of Captain Newport adds complications. Newport tells Smith of an offer from the king to lead his own expedition to find passage to the East Indies. Torn between his love and the promise of his career, the captain decides to return to England. Before he departs, he leaves instructions with another settler. He later tells Pocahontas that Smith has died in the crossing, which leaves her distraught.
Devastated, Pocahontas sinks into depression and still mourns the "death" of her dear, good friend. Continuing to live in Jamestown, she is eventually comforted by a new settler, John Rolfe. He helps her adapt to the English way of life. She is baptized, receives education, and eventually marries Rolfe and gives birth to a son whom they name Thomas. She later learns that Captain Smith is indeed still alive, news to which she has a violent reaction. Pocahontas finds herself rejecting Rolfe and retreats to her loyalty to Smith, thinking fate had spared his life and they were to be reunited. Rolfe and his family are given a chance to travel to England. Arriving in London and sharing an audience with the king and queen, Pocahontas is overwhelmed by the wonders of this "New World." While there, she has a private meeting with Smith.
The reunion is uncomfortable at times. The state of their present lives shows how much they each have changed. Smith admits that he may have made a mistake in choosing his career over his love for Pocahontas. He says that what they experienced in Virginia was not a dream but instead "the only truth." When asked by Pocahontas if he ever found his Indies, he replies, "I may have sailed past them." The two part, never to meet again. Realizing that Rolfe is the man she thought he was and more, she finally accepts him as her husband and love. Pocahontas and Rolfe make arrangements to return to Virginia. Before they depart, she falls ill from pneumonia and dies.
The film ends with images of the young adult Pocahontas and her young son happily playing in the gardens of their English estate. Rolfe, in a voice over, reads a letter, addressed to their only son about his deceased Native American mother. In the film's closing moments, Pocahontas says, "Mother, now I know where you live" with the film fading out over images of nature in the New World.[which?]

Question: What specific relationship does Smith develop during his time as a prisoner  of the Native Americans?
Answer: He falls in love with Pocahontas.