What is the difference between common law systems and civil law systems?

The difference between common law systems and civil law systems seems a little fuzzy to me. The United States is considered to be purely a common law system, but aren't our codified Constitution and the United States Code, in addition to binding judicial precedent, more indicative of a combined common/civil law system? If not, then what exactly sets civil law systems (as in Europe) or combined common/civil systems (as in Louisiana, Quebec, and Scotland) apart from common law systems?

The term common law is ambiguous. It can be used to describe the entire system or it can be used to refer to the case law within a common law system, to refer to the system as a whole a better term might be the 'adversarial system'. This is what we have in England, the United States, Australia, Hong Kong and South Africa amongst others. The main feature of this system is that there are TWO types of law which are binding (case law and legislation) whereas in the civil system, past cases can be taken into account but they are not binding. Another significant difference is that in civil law countries the judge plays a much more important role in determining proceedings, they form part of the case. The Adversarial system emphasizes the debate between the two parties and the judge merely directs the jury and ensures that etiquette is followed. Also, in a civil system academic articles can be considered whereas in our adversarial system an academic article is essentially useless until it is included in legislation. These are the most significant differences.

The legal system in the U.S. is civil law, not common law. In a sense, it's common law because the law is interpreted using precedents, but the actual laws are set by U.S. and state legislatures, so it is civil law.