The difference between Religion and Spirituality is a conceptual boundary issue. To me spirituality falls entirely within the boundaries of what I call religion, like one circle nested inside of another. That is obviously not the case for other people.
I have given some thought to conceptual boundaries of these words and here are my definitions. These are not provided as absolutes that you should automatically except but as central cases for understanding the how people like me categorize these ideas.
As a sociologist my understanding of religion is that it is a world view. (religion = world view.) If one does not believe that one has a spirit - that is just as much of a religious belief as if one did believe. Religious activities are activities that arise out of one's world view. For people who believe that nature is sacred going for a walk in the woods is a religious activity. A taboo is an activity that is forbidden because of a world view. People who don't believe in spirits frequently have taboos against engaging in activities that are supposed to benefit the spirit. i.e. Atheist who refuse to enter churches are responding to a religious taboo (In this case a religious taboo against doing something conventionally considered religious. The irony is delightful.)
I would say that spiritual means concerned with spirit. So spirituality is a measure of ones concern for ones spirit. Most (but not all) traditional religions are concerned about the spirit. The only time ones world view would not include one's concern for one's spirit would be if one's world view precluded the existence of spirit.
When using the above definition all spirituality is necessarily religious but not all religions are spiritual.
When people define spirituality as something other than religion they seen to be confusing a world view with an organization and totally disregarding the fact that religious organizations are made up of individuals joining together to pursue a spiritual path. The vast majority of traditional religions are expressions of the spirituality of their members.
Most people who say they are spiritual but not religious seem to consider religion to be nothing more than mindless dogma and empty ritual. They equate being religious with going to church and doing what one is told as if there were no spiritual bases for these activities. This is a very offensive position to people who consider themselves religious.
People who are members of religious communities know that they are religious and also know that religion is spiritual. People who are not active in religious communities know that they are spiritual but think of religion as being something else. (From the way they talk about it it appears they consider it a form of insanity or other mental derangement)
It is like superstition that way. People call beliefs superstitions if someone else believes them and they don't. No one thinks their own beliefs are superstitions. People who think religion is not spiritual define religion in a way most religious people would not.
Traditional Christianity (which is what most neo-Pagans left) was very Faith based. In the sense of expecting people to accept the reviled wisdom of "God" on faith. An emphasis on a personal relationship with "God" is more of a gnostic position. (New Age spirituality is very gnostic.)
Traditional religions have always had a bit of gnosis (personal experience of the divine) in them. But the trend seems to be to associate the word "religion" with faith based spirituality and the word "spirituality" with gnosis based spirituality. And as you can see that makes even talking about it problematic