Most of Buddhism as it is practiced is clearly a religion even if it does not look like Abrahamic religions, and it certainly is not "a philosophy," except insofar as we conflate philosophy and theology, i.e. not making it less of a religion, though it is certainly true that philosophy is much more central to many types of Buddhism than it is to many other major religions (all of which of course have philosophy but do not make it the central element, prioritizing rituals/worship or personal mystical experience or whatever else, as some popular types of Buddhism also do).

Outside of, maybe, Zen, I would certainly not call Buddhism merely "a way of life" because it has much more particular beliefs about the world outside of one's material personal practice, though again it encompasses many ways of life, as other religions also do.