He won the Cold War by outspending the Soviets, aware that communism cannot compete with capitalism. The Soviets capitulated.
Aside from invading Grenada I remember the 80s as an extremely violent period and Reagan was challenging the Russians everywhere, it was the decade of the American mercenary and Special Ops men around the globe and America supplying arms around the world and challenging and threatening Russia around the world.
Reagan’s muscular and aggressive posture avoided major loss of American troops in major combat (although we averaged about 2200 peacetime military deaths a year during that period) but while his voice was soft, his treatment of Russia was hard.
Trump was similar in his friendly tone towards Russia while militarily building and positioning a war machine against them.