The differences between the Viet Minh and the Viet Cong are both chronological and geographic. The Viet Minh, or, formally, the League for the Independence of Vietnam, was an overwhelmingly but not entirely communist-oriented guerrilla movement formed by Vietnamese nationalist and Marxist-Leninist leader Ho Chi Minh. Formed in 1941 when Ho was residing in China to evade occupying troops of Imperial Japan, the Viet Minh constituted the main indigenous guerrilla force waging war against the Japanese. Following liberation from Japanese occupation, the Viet Minh turned its guns on the French soldiers sent to recolonize what was called French Indochina (Vietnam, Laos, Cambodia). The Viet Minh were instrumental in forcing the eventual withdrawal of French troops from Vietnam, but only after France was humiliated at the battle of Dien Bien Phu, which ran from March to May 1954. In that battle, Viet Minh soldiers, under the leadership of General Vo Nguyen Giap, encircled French forces and, following months of attacks on the French position, compelled the colonial forces to surrender, ending the era of French imperialism in Southeast Asia.
Following France's defeat at Dien Bien Phu and the subsequent end of its colonial reign in Southeast Asia, the United States, very gradually at first and then more rapidly under President Lydon Johnson, moved in to prevent the southern half of the now-divided Vietnam from falling under North Vietnam's communist leadership (still led, until his death in 1969, by Ho Chi Minh). At the head of North Vietnam's army stood General Vo Nguyen Giap, now legendary following his victory in the war against French occupation. Ho and General Giap facilitated the establishment of a guerrilla movement in the south that would be under their control and include both natives of South Vietnam and northerners who ventured into the south. This guerrilla movement was called the National Liberation Front, and was informally known as the Viet Cong. The Viet Cong was supplied throughout the war against the United States and the Republic of Vietnam (South Vietnam) by North Vietnam via the Ho Chi Minh Trail, a long, treacherous series of trails, roads, and rivers that ran from the north through Laos and Cambodia and into South Vietnam. Throughout what Americans called the Vietnam War, considerable effort, including massive bombings, was made by the United States to attempt to stem the flow of weapons and fighters from the North to the South.
The Viet Cong was successful at harassing American and Republic of Vietnam Army troops, and at indoctrinating many villagers across the south in both communist doctrine and in nationalist sentiments directed against the American presence. Using a sophisticated series of underground tunnels to move people and supplies, to provide medical care to wounded fighters, and to launch ambushes against U.S. and South Vietnamese troops, the Viet Cong was a serious thorn in the side of its adversaries. Two factors helped to ultimately minimize its effectiveness. The first was the Central Intelligence Agency's covert action known as the Phoenix Program, which worked to assassinate Viet Cong agents and to undermine its hold on villages. The second was the bloody but militarily successful defeat of the Viet Cong during the so-called Tet Offensive. Tet, the Vietnamese New Year, was the occasion of the January 30, 1968 surprise simultaneous offensive across South Vietnam against Viet Cong units. It resulted in great destruction of the south's infrastructure. Most significantly, the massive Viet Cong uprising gave the appearance to Americans back home of an enormous military setback for the United States. The reality was that the United States and its South Vietnamese allies eventually succeeded in defeating the uprising, but only after nine months of intense and frustrating fighting in the very cities the Americans were supposed to be protecting. The counter-offensive by the U.S. broke the back of the Viet Cong, but the political damage was done, and more Americans began to question the wisdom of the effort.
In conclusion, the Viet Minh was the anti-Chinese and anti-French military force that would be developed into the People's Army of Vietnam. The Viet Cong was North Vietnam's instrument for spreading chaos across the south when the United States replaced France as the principal foreign presence in Vietnam.