I consider myself a spiritual person, but I'm not a religious one. In many circumstances, these two ideas coincide and explain the same concept. However, it shouldn't be a novel idea that someone considers their own self spiritual but not religious. Let me try to explain that a little better for you.
I am spiritual. I am introspective and I self-reflect regularly. At seemingly random intervals, I'll stop in the middle of a conversation and think to myself, what am I really trying to say? I think about my actions and my motives for them–– I think about the way I function–– I try to see what motivates me to do what and I self-criticize myself to help self-improvement. If you do any of these things at all, you're probably more spiritual than you thought you were.
Religion is more of a set "rules" for a culture. It has written behaviors and practices that are set among those that practice that religion. Usually it comes with a book that has a variety of well written stories that teaches the reader a lesson, like humility or the whole golden rule deal. It has set consequences, set characters, set ways to live your life. You can take your religious rules literally or you can apply the meanings behind them liberally. Religion teaches many important lesson and it's definitely something that you should listen to and take heed, but it's not for everyone.
Religion has a teacher, someone that tells you how things started in the beginning, why humans act a certain way, or why there are trees in this world. Someone has to tell you what the religious standards are, whereas spirituality is self-taught and self-discovered. Religion talks about the past a lot and urges you to learn for your mistakes, while you learn more about spirituality living in the here and now. Religion is something for someone to hold onto–– whether they're in desperate need of some help or guidance, religion is there to give you some direction. Spirituality cannot be looked for within others and you cannot find someone else to help you with spirituality. You are your own responsibility and you are the only one in charge of finding your inner spiritual side. Religion is not self-governed–– it is steered by priests, monks, the Pope or others that are "learned" in the way of that religion. Spirituality is self-governed. You make up your own rules as you learn more and more about your inner self and the way that you work. Spirituality is different, personal, and caters to the individual self, so not all people will have the same sort of spirituality. Religion gives a common denominator for all those that practice it. You all identify to practice that same religion.
Overall, religion is a sort of organization, with a set of cultural practices in order to practice that religion. Spirituality is all about the self and introspection. Whether or not you're already a religious person, I highly recommend getting acquainted with yourself on a deeper level. You can experiences spirituality while also practicing your religion, and you can also be a spiritual person while simultaneously being an atheist.
