Mark Oppenheimer distinguishes the level of commitment by whether one uses an adjective or noun as a descriptor:
With Christians, the answer will vary depending on the kind of Christian you’re talking to. Liberal Protestants may say, “I’m Christian,” using the adjective, but many evangelicals, born-again Christians, and other passionate believers will say, “I’m a Christian.” It sounds a little jarring to more secular or liberal types, but not in a bad way. It just sounds hard-core, like the person is planting a flag and standing by it.
For Christians, the difference between “Christian” the adjective and “Christian” the noun is one of both degree and kind. We are all described by many adjectives, but we select very few nouns to sum up who we are. The nouns require a bit more commitment. It’s the difference between “I’m liberal” and “I’m a liberal”—the man or woman willing to own the noun is more committed, for sure. The adjective is what you are like; the noun is who you are.