Christians do believe there are real Christians and fake Christians because the Bible tells us this.

Matthew 7:21-23

English Standard Version

I Never Knew You

21 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven. 22 On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’ 23 And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’