My brother, who recently came back from a mission full of fascinating observations, remarked on this difference he saw in the Church:
When you meet a convert and ask them what it means to be Mormon, they usually talk about belief or doctrine. They talk about how they have a prophet on the Earth today. They talk about Joseph Smith’s personal encounter with the divine and then their own personal encounter with the divine. They talk about new scripture. They talk about the Godhead.
When you meet a “member” and ask them what it means to be Mormon, they usually talk about commandments. They talk about the law of chastity, or the word of wisdom, or tithing. They talk about what you must do to become Mormon.
Not all members who are “born in the Church” are members. Not all “converts” are converts.
Edit: My brother wrote back, “I think what would clarify this is I meant when another Christian asks a Mormon “How are you guys different from us?” gets the response I was talking about.”