Yes, and no.

For the soldier on the ground, it was very similar. A US marine patrolling villages in the Vietnamese jungle in South Vietnam encountered many of the same issues Russian paratroopers would see in the mountains and hamlets of Afghanistan. They were both insurgencies, meaning they fought plains-clothed fighters that disappeared into the terrain or villages. Both Americans and Soviets sought to win over the local population in order to seek out the Viet Cong or mujahideen. On the political front, both sides were embarrassed as armies of poor, uneducated villagers and farmers continued fighting for years, despite taking heavy casualties and fighting a vastly technologically superior enemy. Both the Vietnamese and mujahideen had a history of fighting against occupying empires.

How it differed was that many of the Afghan fighters were simply fighting occupiers or for their local warlord. These local warlords sometimes fought one another for local and regional dominance. In Vietnam, the North Vietnamese pulled the strings of the VC and they fought for a united Communist Vietnam. The US was also leading air and naval campaigns against North Vietnam, which had Soviet technology such as radar-guided surface to air missile systems and jet fighters. The Afghans did not. Their most advanced weaponry was shoulder-launched infrared surface to air missiles, which still inflicted heavy losses on the helicopter-dependent Soviets. The Russians entered the war to put a better leader in power, but ended up staying to keep him propped up and the Americans gradually entered Vietnam to keep the South Vietnamese and a non-Communist government standing.

The Soviet-Afghan War is a fascinating war to study, and I would suggest Afgantsy by Rodric Braithwaite. He gives a history of the prelude to war, the war itself, and the aftermath. It's not dry like some history books, but still provides a thorough understanding of the subject.

Edit: typos