THE COURT OF APPEAL AND AN APPELLATE COURT- DIFFERENCE

These two topic words ( ‘Appellate Court’ and ‘Court of Appeal’) are usually used interchangeably by confusing their meanings and applications.Apart from the fact that both refer to a court of law, they also have one thing in common- ‘appeal’. What then is an appeal. An appeal is a matter brought before a higher court from a lower court in order for the higher court to look into the decision of the lower court on the matter. Thus, both an appellate court and the Court of Appeal hear appeals from lower courts(to appreciate this topic the more, see my post on the hierarchy of courts).
APPELLATE COURT
An appellate court is a court that sits on appeal in a particular case brought before it from a lower court. When an appellate court hears an appeal against the decision of a lower court, it either upholds/affirms or reverses the decision of the lower court. A Magistrate court sitting on appeal on a case brought before it from a customary court is an appellate court as far as the case is concerned. Likewise, a High Court sitting on appeal on a matter brought to it from a Magistrate Court. In effect, there is no particular court named/called an appellate court by the law.
COURT OF APPEAL
The Court of Appeal is the second highest court in Nigeria. In other words, the Court of appeal is the court ranking next to the Supreme Court in the hierarchical pyramids of courts. The Court of Appeal is a creation of the Constitution( Section 237 of the Constitution of the Federal Republic of Nigeria (as amended), 1999. An appeal from the Court of appeal goes to the Supreme Court( the highest court in Nigeria). The Court of appeal also hears appeal from High Courts, Tribunals and some special courts. In other words, the Court of Appeal is also an appellate court. Thus, while the Court of Appeal is a particular court named as such, it is also an appellate court.
CONCLUSION
I will further clarify the difference with three illustrative scenarios.
First scenario- I claimed that you are owing me the sum of N50,000. I took the matter to the Magistrate court to recover the acclaimed debt. I could not prove my case at the Magistrate Court, so the case was decided in your favour(that is, you won). Aggrieved, I took the matter further on appeal to the High court… At this stage, while the Magistrate court is the first court to hear my matter(otherwise known as court of first instance), the High Court is an appellate court. Why? Because, it sat on appeal on my case against you. So, we say the High court is an appellate court, not a Court of appeal.
Second scenario- On appeal to the High Court, the High Court decides in my favour(that is, I won), thus ordering you to pay me the sum claimed. You felt aggrieved and appealed to the Court of Appeal against the High court’s decision… At this stage, the Court of Appeal( being the second highest court) is an appellate court because it sat on appeal on the decision of the High Court. Thus, it is both the Court of Appeal as well as an appellate court.
Third scenario- The Court of Appeal upholds(agrees with) the decision of the High Court and ordered you to pay me the sum claimed. You appealed to the Supreme Court against the decision of the Court of Appeal… The Supreme Court, apart from being the highest court is also an appellate court in this scenario.
From the three scenarios, the High Court, the Court of Appeal and the Supreme Court all acted as appellate courts.While the Court of Appeal is the second in rank in the hierarchy of courts, it is also an appellate court. The High Court can never be the Court of Appeal but it can be an appellate court. 

Questions, suggestions and contributions are highly welcome. Please, check out the meanings of the words in bold in my Mini Law Dictionary.
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