The problem I struggle with is how the world defines "Christian". Most will define it by association with a denominational church. For that reason I do not identify myself as Christian. I once answered Natzarim but that caused all sorts of problems. "Grafted In" doesn't work much better. I guess I'm having a full-blown identity crisis!
Not sure if this helps, and I can't speak to how the "world" defines Christian, but in case you haven't had a chance yet to read Act 11:26, in it, God defines the term Christians as being those who are the disciples and followers of Christ.
(I included only those verses below which seemed relevant to your question.)
[Act 11:20 - 26 KJV]
20 And some of them were men of Cyprus and Cyrene, which, when they were come to Antioch, spake unto the Grecians,
preaching the Lord Jesus.
21
And the hand of the Lord was with them: and a great number believed, and turned unto the Lord.
22 Then tidings of these things came unto the ears of the church which was in Jerusalem: and they sent forth Barnabas, that he should go as far as Antioch.
23 Who, when he came,
and had seen the grace of God, was glad, and exhorted them all, that with purpose of heart they would cleave unto the Lord.
24 For he was a good man, and full of the Holy Ghost and of faith:
and much people was added unto the Lord.
25 Then departed Barnabas to Tarsus, for to seek Saul:
26 And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people.
And the disciples were called Christians first in Antioch.
