The Greek conception of deity and eternity from the golden age of Greece through the coming of Christianity was one rooted in Eternity. Platonic notions of the Ideals, abstracted but concrete (in an idealic realm) and atomic these anchor reality. The Universe was (in their view) eternal and any creator or originator had too be as well unchanging and eternal as those ideals. The truths of these claims were established by the inexorable logic of a philosophical framework on which their civilization/culture was based. Modern deism is very close to these notions with the exception that creation is not, as the Greeks apprehended, eternal but has a beginning (and likely an end). It might be noted I’m unaware of how modern deists deal with the conflict between a God which creates a universe and is at the same time unchanging and eternal (or perhaps the unchanging part is dropped).
The Jewish concepts of deity was concrete by comparison. Rooted in history, prophecy, promise and compact. If not personal it was apprended and comprehended by persons. The history and its narrative validated its truth. A God which speaks to a people or persons in an individual way was seen as incompatible and very different in character from the Greek Ideal for God (or gods).
Modern arguments as they appear between deists, atheists and Christians bring up notions of deity that can be brought into sympathy with both of these two very different notions. That this is impossible is a common mistake that is made in the modern discussion that surround these notions which the following might be viewed as an attempt to bring the Christian viewpoint on the nature of deity into relief (and to contrast with the above).
In the first century AD an individual in Israel and his followers arrived at a new notion of truth and deity which was located in a particular man, Jesus as witnessed him and the events of short span within history. This particular notion was incompatible with both the Jewish and Greek notions of deity and eternity … or they were at first glance. Over the next centuries Christian philosophers and theologians worked out this idea they called the Trinity which surrounded and included all three notions of deity.
The abstract eternal unchanging uncomprehensible deity of the Greek (and essentially the modern deists) is in just about all the essential details known to the Christian as “the Father” as an person/hypostasis of the Trinity. There is no human contact, no touching or comprehending the Father. The problem of a non-eternal universe with an unchanging creator is solved in that the Father via his person enact creation. As John put it, In the beginning was the Word …. and Logos, translated (not-so-accurately as the Word) was Christ, was Jesus (the second person of the Trinity). It was the Word that created … not the Father, who remains unchanged by the act of Creation.
And while this merely touches peripherally on what is understood by Trinity, the point being made is that the deistic God of which the philosopher’s refer, in Christian context is the Father. The personal God that interacts through and within history, that acts and speaks to us is the Son (and for completeness that which moves and acts within us is the Spirit).