The definitions are correct in and of themselves. However you are missing one important point. Although there are millions of people in the world who practice religion in a dry, spiritually void form, religion itself aims to reach spirituality. It gives spirituality a roadmap as it were. I get the feeling that you are saying that religion and spirituality are mutually exclusive, while in reality one lives to give life to the other. When you separate the two, you have either a purely dogmatic climate of values without the life to see them through, or a never ending search for an elusive end.
Where most people miss it is in finding true balance, but often they become too entrenched on their own polarized premises to see any value in the other.