Was Afghanistan really the Soviet Union's Vietnam?

In some ways, yes; in others, not at all. The nickname exists because scholars have cited the Soviet–Afghan War as a significant factor contributing to the dissolution of the Soviet Union in 1991, which is why it is sometimes called "the Soviet Union's Vietnam." In both, a superpower fought with its own troops against opponents who were backed from outside: in Vietnam, the Soviet Union and China supported the North while the US supported the South; in Afghanistan, the mujahideen got most of their external support from Pakistan, the United States (through Operation Cyclone), the UK, China, Iran and the Gulf states.

The Soviets planned a quick job. They meant to secure the towns and roads, stabilize the Afghan government, and withdraw within a year. Instead the fighting dragged from December 1979 to February 1989. Soviet troops held the cities and main roads, while the mujahideen fought a guerrilla war across the 80% of the country not under uncontested Soviet control, mostly rugged mountains. The Soviet presence grew to about 115,000 troops by the mid-1980s.

The scale was different from Vietnam, where US forces rose to 536,000 by 1969. And the cost to Afghans was enormous: one to three million deaths and millions more refugees.