Joseph Stalin did have designs on only Turkey
In the case of Turkey, the Soviet Union had long objected to the Montreux Convention of 1936 which gave Turkey sole control over shipping between the Bosphorus strait, an essential waterway for Russian exports.
When the 1925 Soviet-Turkish Treaty of Friendship and Neutrality expired in 1945, the Soviet side chose not to renew the treaty.
The Soviet foreign minister Vyacheslav Molotov told the Turks that Georgian and Armenian claims to Turkish-controlled territory would have to be resolved before the conclusion of a new treaty1. Following the death of Stalin in 1953, the Soviet government renounced its territorial claims on Turkey.
As for Greece, American and British politicians were concerned about events in Greece and Turkey. From 1946 a civil war had been happening in Greece between its western-backed government and pro-communist forces. Truman gave $400 million dollars to Greece and Turkey and in return established missile bases in Turkey.
Sources:
https://en.wikipedia.org/wiki/Soviet_territorial_claims_against_Turkey
https://www.bbc.co.uk/bitesize/guides/zt8ncwx/revision/6
https://www.bbc.co.uk/bitesize/guides/zgj8fcw/revision/6