1) Anyone following after Christ's Way, is a Christian.
2) As well, anyone who has submitted themselves to Christ, is a Christian.
The difference is; the second, is saved and born again, and the first isn't.
A man WHO is the (1) follower and not submitted.....can one day be a Christian and the next day not.
He is one WHO has started becoming enlightened to the Truth, and then lost faith and walked away.
Judas is a good example of (1).
So perhaps someone told you they were a Christian, because they were following, then stopped, but never announced to you, they were no longer a Christian.
Then again, if you attend church, you have to remember, you sit among sinners, and while they may pretty much be on the same path, that doesn't me they are all at the same distance on the path.
When someone comes forward during the altar call, the question is "Do you accept Jesus Christ as your Lord and Savior." The answer to the question you're addressing lies in this question but it requires some investigation as to what this really means. Many people are anxious to accept Him as their Savior and "punch their ticket to Heaven." Far fewer are actually willing to accept Him as the Lord of their life. That means we follow Him and put His example above all other things in our lives (money, power, politics, nationalism, even our families).
The rich young ruler is a good example of someone who wanted to accept Christ as his Savior but was unwilling to accept Him as his Lord. His lord was money. We are saved by grace through faith, absolutely. Not through any works of our own. We are not saved BY good works but rather are save FOR good works. As Jesus said to Nicodemus, "You must be born again." That means a total change in what you consider important in you life and how you treat others. This was immediately demonstrated by Nicodemus when he gave back the money he had obtained by cheating the people in his role as tax collector.
Jesus also said "A good tree bears good fruit" and "If you love me you will keep my commandments." The Final Judgement scene in MAT 25 underscores the necessity to accept Jesus as our Savior but also to follow him as the Lord of our life. There are many, many people inside the church and outside it that are unwilling to do this. I just read a book entitled "Christian Atheists" which talks about this exact point.