To call the military aviation of the former Soviet Union the "Soviet Air Force" is a misnomer, since the Soviets (and now the Russians) actually had four air forces in their structure: the PVO Strani (National Anti-Air Defense), the Voienno-Vozdushnii Sil (Military Air Forces) and the Strategic Rocket Forces. The PVO was responsible for air defense in all its forms, from flak guns (static or mobile) and surface-to-air missiles to fighter interceptors, as well as the radar systems supporting these. The Strategic Rocket Forces included what in the U.S. Air Force would be missile wings under the Strategic Air Command, but under the Soviet model these made up their own branch of service.
The VVS included everything else military that flew which didn't already belong to one of the two services above or to the Navy, which maintained maritime patrol aircraft, antisubmarine helicopters, and eventually built some half-ass carriers on which they stationed Yak-36 "Forger" fighter-bombers, the Soviet version of the NATO AV-8 Harrier. Fighter-bomber regiments tasked with ground support missions, attack and transport helicopters, transport aircraft to carry desant troops (mechanized airborne units), and long-range bombers that in the U.S. Air Force would be part of the Strategic Air Command, all of these would be under VVS officers - but subordinate to the commanders of the armies and army groups they supported.
This difference in organizational philosophy reflects the Russian/Soviet preference for organizing along functional lines rather than along doctrinal, form-driven lines, and is somewhat similar to the way Nazi Germany organized its armed forces before and during World War II.