Religion to me suggests a "contract" of sorts between human individuals (sometimes entire human communities) and deities. Human beings owe something to the gods (sacrifices, piety, faith, etc), and the gods owe (or at least promise) something in return to human beings (good harvests, salvation, etc).
Where there are no gods, I'd use the term "quasi-religion" to describe the view if there is some supernatural element (such as life after death) to make it "feel" like a religion.
Are Buddhism and Jainism religions?
I think that they would describe themselves as dharmas. But they seem like religions, or at least quasi-religions, for their supernatural elements, such as life after death views.
Does that mean Deism and Epicureanism aren't religions? Scientology?
It's difficult to say if Deism is a religion, but I think it is a quasi-religion at best. I'm assuming here that there is no "contract" between a Deist and his Deity. Neither really owes the other anything.
As for Epicureanism, I don't know of anyone who views that as a religion. It's a philosophy.
Yes, Epicurus accepted the idea that there might be god-like beings out there in the Cosmos, but they are perfectly content to ignore us and think their their divine thoughts. They don't answer our prayers and there is no point in praying to them or worshiping them. The gods aren't even supernatural entities, but are fully a part of our atomic reality.
Epicurus [Internet Encyclopedia of Philosophy]
Because of its denial of divine providence, Epicureanism was often charged in antiquity with being a godless philosophy, although Epicurus and his followers denied the charge. The main upshot of Epicurean theology is certainly negative, however. Epicurus mechanistic explanations of natural phenomena are supposed to displace explanations that appeal to the will of the gods. In addition, Epicurus is one of the earliest philosophers we know of to have raised the Problem of Evil, arguing against the notion that the world is under the providential care of a loving deity by pointing out the manifold suffering in the world.
Despite this, Epicurus says that there are gods, but these gods are quite different from the popular conception of gods. We have a conception of the gods, says Epicurus, as supremely blessed and happy beings. Troubling oneself about the miseries of the world, or trying to administer the world, would be inconsistent with a life of tranquility, says Epicurus, so the gods have no concern for us. In fact, they are unaware of our existence, and live eternally in the intermundia, the space between the cosmoi. For Epicurus, the gods function mainly as ethical ideals, whose lives we can strive to emulate, but whose wrath we need not fear.
Ancient critics thought the Epicurean gods were a thin smoke-screen to hide Epicurus atheism, and difficulties with a literal interpretation of Epicurus sayings on the nature of the gods (for instance, it appears inconsistent with Epicurus atomic theory to hold that any compound body, even a god, could be immortal) have led some scholars to conjecture that Epicurus gods are thought-constructs, and exist only in human minds as idealizations, i.e., the gods exist, but only as projections of what the most blessed life would be.
No one views Aristotelianism as a religion either, despite the stated view that some sentient "Prime Mover" exists. We don't have a "contract" with the Prime Mover either, and it is a natural entity despite its metaphysical peculiarities.
As for Scientology, it is arguably a quasi-religion in that it has many supernatural views, such as the existence of body thetans and life after death.
Secular Humanism may provide some social glue, but it just doesn't feel religion-like enough for me to see it as a religion. There are no deities and no supernatural views. I count it as a philosophical community instead.
eudaimonia,
Mark