Morality and law are two different concepts that many times converge into one but are not necessarily dependent on each other. A person could be law abiding and immoral, be both moral and law abiding, not moral and not law abiding, or immoral and not law abiding. The four categories represent possible combinations of law and morality and how they relate and interact.
The law is a lower copy of morality. Laws must always seek to represent the general moral sentiments of society or they are no longer supported by the culture of a country. If laws fail to adapt and change with each generation they run the risk of losing public trust. In essence, laws should be better carbon copies of the beliefs of society.
As morality is a deep seated belief system it is purer than its reflection. Those who define their morality based upon law alone, and whether or not they can be punished for breaking it, are not necessarily moral. They follow the law based upon its personal interest to them and not any sense of value beyond the law.
For a person to be truly moral they need to follow their inner compass on issues and matters of right and wrong. If they only follow the law then they are limited to a lower form of human development based in cold rules and processes. They have not yet been able to develop the ability to think independently about their obligations to society.
Consider corporate scandals where even though solid legal advice is followed the damage to society and public trust was massive. Those with an internal sense of values might have avoided the situation completely, turned in the activity, or removed themselves from the situation. Law and morality are related but often separated by depth of one's values.
Law Abiding and Immoral: A person who follows the law while cheating its spirit. They use power-driven attorneys, knowledge of the law, and subjective application of the law to fulfill their own needs. They may not break any laws but at the same time leave a wake of destruction for their selfish purposes. The law is seen as a game for manipulation.
Moral and Law Abiding: A person who finds value in following the law but also has morality beyond the law. The law works as a guide and is followed in so much as the law is moral. The order the law provides is congruent with their basic value systems. When laws are in harmony with the values of the people there is a sense of legal peace with the population.
Moral and Not Law Abiding: There are times when a person must be moral and not necessarily follow the law. For example, if the law is immoral or is a transgression against the rights of the people then moral people have no need to follow the law. For example, Germans who helped Jews survive in WWII Germany may have violated the law but acted on a higher moral authority.
Immoral and Not Law Abiding: There are people in the world that are both immoral and not law abiding. These are your sociopaths and pathological criminals who don't care about morality or the law. Anything that steps in the way of their needs fulfillment are discarded as useless. You will find them not only imprisoned on a regular basis but also creating victims wherever they go.