The Christian martyr is an entirely different thing. He is a devoted follower of Jesus Christ, but has no idea of doing any harm to his neighbors.
The modern martyr kills himself in the pursuit of his own pleasure, profit or purpose. The suicide bomber thinks he will ensure his place in paradise and various rewards. The suicide shooter at the mall thinks he will be famous and will no longer need to face the difficulties of his life.
The Christian martyr wants nothing more than to live for the glory of God by displaying the fruit of the Spirit of God -- "...love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness, and self-control." (Galatians 5:22-23) He is already assured of his place in heaven and knows he will arrive there when God wills it to be so.
The modern martyr wants to take other people with him. He will do as much damage as he possibly can - not in battle against armed assailants, but in a massacre of innocents. The more bloodshed and destruction, the better.
The Christian martyr wants to take other people with him too - but not in a violent attack. Rather, the Christian martyr wants other people to join him in being followers of Jesus Christ. He pursues this through a life of faith and godliness - loving God and loving his neighbors.
The modern martyr chooses the time for his death by his own actions. When he triggers the detonator - it is time. When he carries weapons into a school - it is time.
The Christian martyr is willing to die if the only other option is to betray the Lord Jesus. But his death will not be at his own hands. Those whose spiritual ancestors killed Jesus Himself are the killers of the Christian martyrs too.
The Christian martyr is willing to live and not afraid to die. While he lives, he devotes himself to living in obedience to the word of God which says, "Love your neighbor as yourself" and "Love your enemies" and "bless those who persecute you - bless and do not curse." (Leviticus 19:18; Matthew 5:43-44; Romans 12:14)
The Christian martyr lives by God's word and for God's glory.
(Romans 12:19-21) Beloved, do not avenge yourselves, but rather give place to wrath; for it is written, “Vengeance is Mine, I will repay,” says the Lord.
“If your enemy is hungry, feed him;
If he is thirsty, give him a drink;
For in so doing you will heap coals of fire on his head.”
21 Do not be overcome by evil, but overcome evil with good.