The United States shares a common legal heritage with England primarily due to the English Magna Carta of 1215. Although there were subsequent versions written after the 1215 document, the 1215 document written by English nobles forcing the king to give up power was a successful first in human history. Many of the principles of the Magna Carta were adopted by the United States and are regarded as sacred to American freedoms. The backbone of Magna Carta is the principle stating that no one is above the law.....this includes the king. The idea that a power, any power would now be subject to interpretation and or scrunity by others changed the course of human history. (The Watergate Scandal involving President Nixon is a prime example of that principle in action.) Furthermore, Magna Carta guaranteed trials to the accused and that those trials be subject to a jury of peers. The document also defined cruel and unusual punishment (historically referred to in England as the four deaths) prohibiting any such treatment previously described as such for the accused and convicted.
There is one exception to this common heritage, and that is the origin of law in the state of Louisiana. If you recall, the state was part of the territory purchased in the Louisiana purchase, and the origin of law in that area is French, not English. The Napoleonic Code governed. As a practical matter, there is not all that much difference in the administration of the legal system or the practice of law today in Louisiana. It is and always has been subject to the Constitution and its Amendments. But there are differences in how things are named. For example, I believe that whereas the rest of the United States has counties, Louisiana continues to have "parishes." Perhaps someone who practices law in Louisiana will be able to point out some of the other different terms still used there.
What our legal system has in common with England, mostly, is the idea of the "common law."
The common law was a set of legal ideas that was developed over a long period of time in England. In England, this law began developing even before the Norman Conquest.
The ideas contained in the common law were not made by legislatures. Instead, they were made judges handing down decisions. These decisions would then come to be applied to similar cases. Through this process, legal doctrines came into being.
The US and England also share a legacy that goes beyond the common law -- jury trials, the idea of rights that comes from the Magna Carta, things like that.