Yes, what you say makes sense. Believing oneself to be "religious" or "spiritual" is purely perceptional
from the person and others who are observing the person. The proof is in the pudding, as they say.

I have met some religious people who I felt were quite enlightened. Yet, more enlightened people I have met consider themselves spiritual.

I don't suppose it really matters much. The question need not be asked; the answer lies in a person's whole package: their thoughts, feelings and deeds. A good clue into the nature of a person's soul is to observe their ability to give - of themselves and their possessions.

Just a mere thought this evening.