At the close of the 20th century, there are literally dozens of schools of thought about the best method of studying what it is to be human, and to be in relationship with the Unknown. Some critics have noted that spirituality puts God in the center of things, while psychology elevates the human being to that position. This is different from though often in alignment with religion. Spirituality is a private, internally originated experience, whereas religion is a shared, externally manifested experience. The difference is one of I feel versus we believe and do.
Spirituality is the path of the heart.
Transpersonal psychology aims to ask the disciplined questions that lead to scholarly understanding of spiritual experiences. It is the path of the head. Another way to look at the difference between spirituality and transpersonal psychology is perhaps to use the being versus doing analogy. I would posit that spirituality is a way of being, a lifestyle of the heart resonating with Great Spirit. Transpersonal psychology is the application of methods and mental concepts that bring understanding of what that resonating experience is all about.