Case law consists of the written opinions (or decisions) of courts as they resolve litigation. Opinions explain the reasoning behind the resolution, including citations to relevant statutes and other cases (precedents).
When you're looking for a court case, what you're really looking for is the court's opinion for that case. Case, opinion, and decision are used interchangeably.
Why are there so many cases with the same name?
There are several possible explanations:
|United States District Court||Superior Court|
|United States Court of Appeals||Appellate Court|
|United States Supreme Court||Connecticut Supreme Court|
FYI: In the federal court system, Connecticut is in the jurisdiction of the Federal District Court of Connecticut, 2nd Circuit for the U.S. Court of Appeals (along with New York and Vermont), and the United States Supreme Court. In addition, there are also special federal courts like bankruptcy courts, U.S. Tax Court, and U.S. Court of International Claims.