This might help...
The best of the best, the lawful good character acts on the side of goodness, righteousness and order. The warrior who is beholden to a lord or a church, the priest dedicated to healing the wretched - anyone who cannot stand by while others suffer. They will chase evil to the end of the world.
The lawful good character will always strive to do good. However unlike chaotic good, they refuse to go against any laws to pursue said good action. Therefore they will not murder an innocent in sacrifice to a greater cause.
The hater of chaos, a lawful neutral character will stick to the letter of the law, whether it is their personal code of rules, their king's, or their religion's. This character finds chaos as abhorrent as evil and will not bend their personal guidelines even to help another if it will contribute to chaos.
A being who gains power through methodically destroying others is lawful evil. Power comes through order, but one can be orderly about slaughtering innocents. Tradition is important, but goodness is not.
Ultimately a giver, the neutral good character will do what they can to help, working within law or chaos; but ultimately they prefer their own counsel.
A middle-of-the-road character, a neutral character finds it difficult to fit into any other distinction. They do what seems to be a good idea, whether it flows with law or chaos, good or evil. Often a follower and at times superb leaders, they'll rarely go against the group.
A neutral evil character serves only their own needs/ends. They follow no law but also have no drive toward chaos. They kill or steal as they see fit to get what they want.
The hero of the downtrodden, the chaotic good character cares not for laws and order but only for doing good. If they must break the law to help others, they will do so without compunction. This character will steal to feed a poor family or stand up to their own master to defend a falsely accused servant.
The true individual, the chaotic neutral character prizes their own freedom above all else. They do not want ties to either good or evil to influence them, preferring to make their own way as they see fit. Most chaotic neutral care nothing for people in their groups, have little to no allegiances, caring only for themselves.
With the drive of pure hatred, the chaotic evil character will do whatever they can to attain their goals. They are bound by no laws, no master and no compassion. While unlikely to run down the street slaying innocents (chaotic evil does not mean stupid), this character would have no regrets about doing so.