1st of all, it seems the Jews' concept of salvation was a Messiah leading them to throw off the yoke of oppression from Rome and Jesus disappointed them with his turn the other cheek, walk a second mile, don't live by the sword teaching. They may have gotten that from the OT, I'm not sure.
The NT concept of salvation and eternal life looks like this: love God and man and you will inherit eternal life. That life starts today if you turn from your evil ways and stop living in wickedness and continues as one gets set free from the bondage of sin which brings death. If one walks in the light, rises up to walk in newness of life, and continues therein until death then this eternal life carries forward into the afterlife.
This is how Jesus put it in Mt. 25:34 and Lk. 10:25: hen shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
35 For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:
36 Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.
And, behold, a certain lawyer stood up, and tempted him, saying, Master, what shall I do to inherit eternal life?
26 He said unto him, What is written in the law? how readest thou?
27 And he answering said, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy strength, and with all thy mind; and thy neighbour as thyself.
28 And he said unto him, Thou hast answered right: this do, and thou shalt live.
None of this has changed since then.