Final answer:
Premier Mikhail Gorbachev gave the West the terms 'Perestroika' and 'Glasnost', with 'Perestroika' focusing on economic restructuring and 'Glasnost' on political openness. The 'Iron Curtain' and 'Cold War' were terms already in use and not coined by Gorbachev.
Step-by-step explanation:
The term Premier Mikhail Gorbachev gave to the West was "Perestroika" and "Glasnost". The term "Iron Curtain" was coined by Winston Churchill to refer to the division of Europe into Communist-dominated Eastern Europe and the West after World War II, and does not originate with Gorbachev. The "Cold War" is the period of geopolitical tension between the Soviet Union and the United States, which lasted from the end of World War II until the collapse of the Soviet Union in 1991, but is not a term coined by Gorbachev. Gorbachev's policies of 'perestroika', which means restructuring, were aimed at reforming the Soviet economy, and 'glasnost', meaning openness, intended to foster a more transparent and less repressive society.