These are both just labels. It's like asking if Americans really Americans? Or going back farther, are Native Americans really Native Americans if most historians/anthropologists assume they traversed from Asia to get to North America?
Going by the broad definition (Believing in Jesus and living your life--as well as you can--following His example), yes we are "Christians". However, not all "Christians" are Christian. More people claim to be Christian than actually are living a Christian life. Some people don't follow Christ yet still call themselves Christian.
It is impossible to be perfect. That's not what Christianity is anyway...That's Buddhism. The Bible says that it's by Grace that we are saved because we could never be perfect and therefore "works" are not the way into heaven. The Christian belief is that you can't be Jesus and that's why you need Him. Accepting his grace is becoming Christian. Accepting him means recognizing your sin and asking for forgiveness. This doesn't mean you will suddenly become "like-Christ" but you must then TRY to be more like Him. So, as long as you've accepted Jesus and you are TRYING to please Him then you are probably a Christian.
Short and simple. If you surrender your life to christ, believe that he died for you on the cross, and know he is lord of all, you ARE his and HE is yours. It doesn't matter what you do in life, he will accept you into paradise if you accept him now.
To be Christian is to hold yourself to a very high standard. It is not just to slap on a label and show it to anybody, as an admittance to a club. If you feel the need to defend any actions by Christians or your own, is probably a sign that you know you are not living up to said standards.
No one can measure up to the ideals that are expressed in the bible whether it is interpreted literally or symbolically. The epistles say several times that we must deny ourselves and die to the flesh and be completely selfless and christ like. It says several times elsewhere that what is labelled as sin (which would be better understood as us making mistakes) separates us from God and until one repents they are cut off from His love and are hell bound.. Many believers state that no one is good enough without Jesus but the truth is in this religion no one is good enough period.
The Apostle Paul was the best person that has been close to be Christ-like. (2 Corinthians 11:21-33) "Whatever anyone else dares to boast about—I am speaking as a fool—I also dare to boast about. 22 Are they Hebrews? So am I. Are they Israelites? So am I. Are they Abraham’s descendants? So am I. 23 Are they servants of Christ? (I am out of my mind to talk like this.) I am more. I have worked much harder, been in prison more frequently, been flogged more severely, and been exposed to death again and again. 24 Five times I received from the Jews the forty lashes minus one. 25 Three times I was beaten with rods, once I was pelted with stones, three times I was shipwrecked, I spent a night and a day in the open sea, 26 I have been constantly on the move. I have been in danger from rivers, in danger from bandits, in danger from my fellow Jews, in danger from Gentiles; in danger in the city, in danger in the country, in danger at sea; and in danger from false believers. 27 I have labored and toiled and have often gone without sleep; I have known hunger and thirst and have often gone without food; I have been cold and naked. 28 Besides everything else, I face daily the pressure of my concern for all the churches. 29 Who is weak, and I do not feel weak? Who is led into sin, and I do not inwardly burn?
30 If I must boast, I will boast of the things that show my weakness. 31 The God and Father of the Lord Jesus, who is to be praised forever, knows that I am not lying. 32 In Damascus the governor under King Aretas had the city of the Damascenes guarded in order to arrest me. 33 But I was lowered in a basket from a window in the wall and slipped through his hands." What kind of Christian brags about their suffering in Christ's name? Instead they complain for the smallest things. Paul did what Christ said to do. (Matthew 5:11-12) 11 “Blessed are you when people insult you, persecute you and falsely say all kinds of evil against you because of me. 12 Rejoice and be glad, because great is your reward in heaven, for in the same way they persecuted the prophets who were before you." Also Jesus command Christians in (Matthew 5:43-47) 43 “You have heard that it was said, ‘Love your neighbor and hate your enemy.’ 44 But I tell you, love your enemies and pray for those who persecute you, 45 that you may be children of your Father in heaven. He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous. 46 If you love those who love you, what reward will you get? Are not even the tax collectors doing that?