When the war ended, circumstances in Greece were unfavorable to the maintenance of civil peace:

EAM was in control of nearly all Greece. Its leaders numbered many excellent liberals, the most eminent being Professor Svolos, a Socialist; but the Communists were clearly dominant. The returning Greek army was under the control of rabid, uncompromising monarchist officers... Had the issue of Greek sovereignty been left to these two Greek forces, there is no doubt of the outcome. The ineffectiveness of the returned Greek monarchist army was shown when, at the end of 1944, civil war broke out in Greece. ELAS surrounded the monarchist army and immobilized it from the outset.

However, they were not left to their own devices, and instead they were influenced by outside forces from Britain and Russia and from other circumstances that altered the way Greek society reacted.

Howard K. Smith sees the decisive force in what occurred as being the entry of British troops as the Germans left. He says he would like to be generous and assume that the British wanted to bolster the middle-of-the-road and democratic forces in the country to create a basis for democracy, but there is no real evidence to support this. Instead, it seems that the British were determined to destroy the EAM and to install the discredited monarchy in power, along with its rightist supporters.

The Spanish Civil War developed during the 1930s as a conflict between major social and economic interests, specifically the landowning class supported by the military...

Outside forces took some advantage, though the tensions were real and predated entry by communists or any other political force. In Greece, the tensions were not as deep and might have worked out their problems had not a succession of outside interventions taken place, first with the Germans during the war, then with the British after the war, and by the Russians using the occasion to counter the British. The American intervention came much later and fell on the side of the ruling party largely as a counter to the communists. Both conflicts were protracted and highly damaging to the economies of each country and to human lives. Both also produced a long-standing right-wing government that repressed opposition and prevented democratic reforms for many years, even for decades. The political consequences continue to some extent to this day.
Bibliography

Anderson, Paul, "Why Did the Spanish Civil War Start in July 1936?" History Review 48(2004), 36-40.

Bolloten, Burnett. The Spanish Revolution: The Left and the Struggle for Power during the Civil War. Chapel Hill, North Carolina: University of North Carolina Press, 1979.

Kousoulas, Dimitrios G. The Price of Freedom: Greece in World Affairs, 1939?1953. Syracuse, New York: Syracuse University Press, 1953.

Smith, Howard K. The State of Europe. New York: Knopf, 1949.

Stavrianos, L.S. Greece: American Dilemma and Opportunity. Chicago: H. Regnery Co., 1952.

Sweet-Escott, Bickham. Greece: A Political and Economic Survey, 1939?1953. London: Royal Institute of International Affairs, 1954.