Ho Chi Minh City and Saigon are simply two names for the same general place. The city now known as Ho Chi Minh City has been inhabited for many hundreds of years, and its name has changed a few times in that period, as ownership has shifted between nations.
Early on the area was known by the Khmer name Prey Nokor. The name Saigon was used in an official context as early as the end of the 17th century, when Lord Nguyen Phuc Chu sent a servant to form a government there as a southern outpost for Vietnam. After the French colonized Vietnam, the name Saigon was used almost exclusively as the name for this city – although it is more commonly written as Sai Gon, to more accurately reflect the Vietnamese naming conventions.
The origin of the name Saigon is open to some debate, but most people hold that it originates from the Khmer Prei Kor, which simply means city of kapok trees, and would be a fairly accurate description of the area in the past. The Vietnamese translation of this term would be roughly Sai Con and it is easy to see how this could then evolve into Saigon.
During the war which took place from the mid-1940s to the mid-1970s, the man Ho Chi Minh played an integral role. After spending some time in China and the Soviet Union throughout the 1920s and 1930s, he returned to Vietnam and spearheaded the independence movement. After convincing the Emperor of Vietnam to step down, he took over as the Chairman for the new Provisional Government. After the eventual defeat of France in the 1950s, he became president of the new North Vietnam, guiding it through the war that would follow.
Though he died in 1969, Ho Chi Minh remained, and remains, a cult hero for many in Vietnam, particularly in the Communist leadership. He is still referred to as Uncle Ho by many in Vietnam, and his likeness appears throughout the country. It was this adoration and admiration that led to Saigon being rechristened, in 1975, as Ho Chi Minh city.
Although this is its official name, and although Ho Chi Minh is still venerated, to many, if not most, the city will always remain Saigon. It is Saigon that is the name given to the city in so many romantic works of fiction. It is Saigon used in the old movies and musicals. Somehow Saigon seems to wrap itself in a shroud of beauty and mystery, while Ho Chi Minh City seems utilitarian, and sparse. In the same way that for some Sri Lanka will always remain Ceylon, and Myanmar will ever be Burma, so too is Ho Chi Minh City destined to always be known as Saigon.