Spirituality can include religion, but doesn't need to. A spiritual practice is one where we are putting ourselves in good position to better understand our true nature and self, our spiritual side, as opposed to only considering the material side of things.
Many religions have practices or teachings that can produce this type of realization, but that doesn't mean they always produce results. There are many people who are religious, but wouldn't be considered spiritual. Growing up Catholic showed me this quite clearly, I ended up close to atheist for a while before I found my spirituality , my connection to what I would consider the true self, not the ego. Spiritual practice is ALWAYS personal practice, because we can't know someone else's experience completely.
My $0.02