In the US federal system, they are known as appellate courts. If you are asking about another system, you'll need to explain that.
Workhorses
In the federal Judicial Branch, the intermediate appellate courts are the thirteen US Court of Appeals Circuit Courts. The states use different naming conventions for their intermediate appellate courts.
appeals courts
Yes, that is why the court is "supreme."
(in the US) there is no such court officially designated"The Intermediate Appellate Court," there is no such jurisdiction.The US Courts of Appeals Circuit Courts and their state equivalents (one step down from the state supreme courts) are often referred to colloquially as "intermediate appellate courts," which simply means they are the appeals courts that act as a buffer between the trial court and the supreme court in a given judicial system.
federal statute
Federal and state supreme courts (or their equivalent) are the highest appellate courts in their jurisdiction and have authority to make the final decision on a case under review.Supreme courts usually have what's informally known as "intermediate appellate courts" immediately below them. In the federal judiciary, the US Supreme Court is higher than the thirteen US Court of Appeals Circuit Courts (intermediate appellate courts).Some of the differences are:The Supreme Courts set binding precedents for all courts in a given state or nation, whereas intermediate appellate courts only set binding precedents fewer courts or a smaller territory.Supreme Courts have much more latitude (discretion) over the cases they hear; intermediate appellate courts have mandatory jurisdiction over more types of cases.There is usually only one supreme court for a given state or nation (although Texas has two), but many intermediate appellate courts.The intermediate appellate courts here more cases.Supreme courts consider cases en banc (as a full court); intermediate appellate courts are more likely to assign one judge or a three-judge panel to review a case, although they do occasionally hear cases en banc, as well.
Japan has an independent judicial system patterned on the American model, with trial courts at the local level, several intermediate appellate courts, and a Supreme Court.
municipal
These courts enable the state's highest court to concentrate on a few cases; guide trial courts; & point the way to law changes
intermediate scrutiny
Marlin O. Osthus has written: 'Intermediate appellate courts' -- subject(s): Appellate courts, States
Courts of Appeals is the intermediate-level federal court the courts of appeals is considered the workhorse of the court system.