Also, there are people who say they have trusted Jesus or become a Christian, but that belief is based on the beliefs of their family or them wanting a "get out of jail free" card or some other non-internalized belief.  The Bible says that "the demons also believe, and shudder." (James 2:19b).  It isn't enough to just believe that God exists or that Jesus exists.  You have to admit who He is, His character, our sin, and repent of that sin and submit to His will and authority.

There will be plenty of people who consider themselves Christians, but who are not.

"21 “Not everyone who says to Me, ‘Lord, Lord,’ will enter the kingdom of heaven, but he who does the will of My Father who is in heaven will enter. 22Many will say to Me on that day, ‘Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?’ 23And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness.’"  (Matthew 7:21-23)

I guess you could call them the illegal aliens.  Jesus calls them the tares among the wheat.

I do believe that a person can truly know that they are saved and a child of God, but we cannot know for certain on another person, although we can have a pretty good idea by their fruits.