There are people who say that there is no practical difference in respecting and even following a school of philosophy like Epicureanism or Stoicism and in following a religion. However, there is one crucial difference. The most important single thing is that there is nothing supernatural in Epicureanism or many other ancient schools of philosophy.
Epicureanism and Stoicism are only human constructions in which people suggest that a certain way of thinking and living will benefit humans who follow these ideas. They can well be seen as religions also, but they are not at all religions in the way Christians or Muslims or Jews do see religions.

In some forms of Stoicism, there is also a belief in a Pantheistic life force or Nature, but this life force does not dictate big books for humans to follow to the letter or tell them what they should eat. In Epicureanism, there are not even these Pantheistic connections present. The questions of existence or non-existence of “gods” is simply brushed away as irrelevant to real life of humans. Epicureanism is in the end only interested in making real life of real humans better.
The big difference is that it is a quite different thing to say that something is an inerrant word of an omnipotent "god" or to claim that something is an extremely wise piece of advice for a certain group of humans.

Of course, also religions do contain many wise things. However, these pieces of wisdom are commonly sold as the "only possible truth". Of course, also a philosopher very naturally thinks that he has gotten the right answer. He would not be peddling it to others if he would not think it to be the right answer.
However, a philosopher is normally not suggesting that there cannot be any other wisdom than his. However, this we can say only if we forget Aristotle for a moment. Aristotle namely did think that he had got it all absolutely right, even if he way off the mark in very many things.

There simply is a big difference in believing that you must follow the inerrant words of an angry and demanding "god" that are revealed in some kind of a "holy book" to the last letter, or in believing that a sage whose wisdom you personally have come to trust has found a way of making your life a little more bearable if you follow his advice.

Wikipedia

We are comparing schools of philosophy mainly to Christianity here. However, the bad old Christianity still is THE religion in our own western society. That includes all of the nations that live in the lands that happened to fall under the iron rule of the Christianity through some historical and political coincidences.
Christianity was also btw. the very religion that did destroy the Stoics and Epicureans. Christians did it so thoroughly that ultimately not a single one remained anywhere in the Christianized Roman empire.

Judaism and Islam (and even Mormonism) are built on the very same basic principles as Christianity. Quite another thing of course is how people act on the basic rules presented by religions. All of these religions have diversified into a veritable tangle of different belief-systems and people have different levels of attachment to them.
Most of all many modern people do pick and choose individual things from them to create their private religions. All of the Abrahamic religions or Judaism, Christianity and Islam are, however, based on the same basic assumptions of there existing an unmoving "absolute truth". This 'truth' is normally revealed in the "holy book" of that religion and only in it.

In modern times, however, there exists a increasing number of people in all religions who disregard these basic ancient demands for uniformity. These people can even respect the wisdom that is present in other religions or in secular philosophy
However, in all of the Abrahamic religions there still exists a basic requirement of accepting the existence of a single absolute truth represented by that religion. Everyone who strays from this requirement is easily accused of corrupting the very core message of that religion.

In philosophy, such requirements do not exist, and this basic fact will always differentiate philosophy from religions. However, if any philosophy claims to be the carrier of an absolute and final truth, it is not merely a philosophical system anymore , but a religion. Basically it is as simple as that.
The goal could just be to make people realize that religions are just opinions of how things ought to be. In a free society, they are, in theory, free to choose a religion that suits their personal needs.

One should bear in mind that philosophical systems like Epicureanism and Stoicism were often chosen according to a personal adult decision in their time. Of course, undoubtedly there was with time also the force of tradition at play even among them.
Admitting that also all religions are just human ideas like philosophy would of course be an unbelievable revolution in the world of religions. It is not realistic to expect such a miracle to happen. At least Christianity, Islam and Judaism would lose their main selling points. They are after all offering extremely comforting claims of full certainty in a world that is so full of uncertainty.

Epicurean philosopher Epicurus is in Facebook at:
http://www.facebook.com/epicureanphilosopher

Stoic philosopher-emperor Marcus Aurelius is in Facebook at:
http://www.facebook.com/aureliusphilosopher

More info on Epicureanism:
http://en.wikipedia.org/wiki/Epicureanism

More info on Stoicism:
http://en.wikipedia.org/wiki/Stoicism

(This piece was completely refurbished on 9th of November, 2012)