"Greek religion: religious beliefs and practices of the ancient Hellenes. Greek religion is not the same as Greek mythology, which is concerned with traditional tales, though the two are closely interlinked." Encyclopædia Britannica: Greek religion, in: Encyclopædia Britannica Online
Ethnic Hellenism: the culture of the ancient greeks and polytheistic Greeks (ethnic Hellenes) of the Christian era.
Hellenismos is the name of the Greek Religion. "Hellenism is a package consisting Ethos, World View, value system" (Vlassis Rassias), language, customs, philosophy, community, and Religion. Hellenism is something that is called "Ethnicum" (sadly, most people would call it just "Paganism"). "Hellenism is a way of human functioning at the collective and personal level." (Rassias). Hellenismos is only one (!) part of the Hellenic Ethnicum. The Ancient Greek Culture was the product of the Hellenic Ethnos, and the same applies to the Hellenic Religion. Therefore the polytheistic Greeks are called since late antiquity and they still call themselves as "Ethnic Hellenes", because, and in contrast to the christian Greeks, they follow the ethnic and genuine hellenic Tradition, Religion, and Worldview created by the Ancient Greeks themselves. The identity of the ethnic Hellenes is culturally, ethnically, and religiously. Someone is called "Ethnicus" (lat.) or "Ethnikos" (gr.) (pl. Ethnikoi) when he follows the genuine and indigenous Ways of his Ancestors. "Hellenic Religion" is not an umbrella Term. The many terms Hellenic Polytheism, Greek Religion, Hellenic Polytheism, Hellenismos, and ethnic hellenic Religion are synonymous and they are all used interchangeably to refer to the one and the same religion. The term "Reconstructionism" (unknown to the most Hellenes in Greece) refers the methodology of reviving ancient ethnic Religions. The hellenic Organizations YSEE, Labrys, Thyrsos, and the Societas Hellenica Antiquariorum (native hellenic groups) hold the vast majority of practitioners of the Hellenic Religion in the world. The Hellenic Religion has nothing to do with the so-called "Neo-hellenic Polytheism" and with "Neopaganism" in general.
"Hellenismos": From Ancient Greek Ελληνισμός (Hellēnismos, "imitation of the Greeks") Meaning: 1. religion of the Greek divinities, 2. Greek culture http://en.wiktionary.org/wiki/Helleni...
Meaning of the Term "Ethnicum/Ethnicism": 1) The religions of the Gentile nations of antiquity 2) Heathenism; idolatry. 3) (in the senses: Gentile): from Late Latin ethnicus, from Greek ethnikos http://www.encyclo.co.uk/define/Ethni... http://www.merriam-webster.com/dictio... http://dictionary.reference.com/brows... http://en.wiktionary.org/wiki/ethnicus (Ethnism should not be confused with the irrational modern creation called "Nationalism" (identification of Ethnos with nation state); an anti-ethnic ideology, which is opposed to Ethnism and the natural ancient Ethnodiversity. Hellenism is an Ethnism and Hellenismos is an ethnic Religion ergo incompatible with homogenizing Nationalism and Absolutism. Hellenismos also states, that it is the duty of all mentally healthy Humans to stand up for Ethnodiversity and against all Systems, trying to abolish the ethnic cultures, their diversity, and way of lives for the sake of homogenization.)