To put /u/itsallfolklore in other words. Religion and myth are not one and the same. To make an analogy we would not call the Bible (either the Jewish Bible or the Christian one) religion, on their own they are like Greek myths, stories that form the basis for the religion, that explain the origins of man, the world, provide moral guidance, etc. Religion involves actual practices, often these are not necessarily in the sacred scriptures. Greek religion then is a bigger thing than Greek myth, and involves a variety of practices and beliefs that may be tied to Greek mythology, but are nonetheless separate.

We need to separate "belief system and expressions of devotion" from "mythology." Mythology is a tough term (see excerpt below), but we really need to take that to mean a collection of stories, some of which have to do with the gods and some of which are simply heroic stories that are part of a cultural inheritance, not linked necessarily with belief.

The following is an excerpt from my Introduction to Folklore, which may help:

Something also needs to be said here about myth. People use this term awkwardly. In a European context, myths tend to be the artificial constructs of ancient and Classical-era priests or literate people who sought to weave folk traditions into a comprehensive whole. The exercise often had political purposes, designed to provide diverse people with a single set of beliefs and stories. By reconciling similar traditions, the shared culture of these groups could be seen as more important than the differences, justifying the central rule of the king and his priests. Myth is also a way of organizing and reconciling folk traditions, which by their nature can be contradictory and highly localized. Myth tends, however, to make gods of supernatural beings, giving those powerful entities a status – for modern readers – similar to the Judeo-Christian-Islamic God, even when this comparison is not justified. Of course, it is also important to point out that myths were stories that were told – and then written down – and they were different from religion itself. Many myths were simply the shared cultural inheritance of a group of people.

To the second part of your question; the ancient Greek belief system and devotional practices were replaced (or subsumed in some ways) by conversion to Christianity (although that was not the first eastern religion to make inroads).

In my folklore classes, I discourage the use of the term "mythology" because it can be insulting. I had a student who insisted on referring to American Indian "myths", and it was hurtful to my Native American students - who stated as much. I pointed out that we can talk about the "Resurrection story" without insulting anyone, but when we call it the "Resurrection myth" there is likely someone who will be insulted. But for the ancient world, as long as we recognize the limits of the term, using "mythology to describe a group of primary sources is probably OK; not likely to be a lot of offended ancient Greeks.