In US legal jargon, the 'referring court' seems to be the court that referred responsibility for carrying out a particular act to a commission or agency to carry out, not necessarily a court at all. In a number of law reports I looked at from the State of Texas, a referring court was a court in which an appeal case (case being reviewed) was being heard, so an appeal court (with a small 'a'(English)) was also the reviewing court (court reviewing a case). However Court of Appeal with large letters seems (from what I saw) to be the specific name of a higher tier of court(s) that are appealed to (review cases), and it is possible (I got the impression from what I read) that lower courts not called by that name also review cases (are appealed to and so are review courts) when the law says that it is within their competence.

In the below example, which is in a court which is called an Appeal Court (but as said, some lower courts reviewing cases, may not be) the same court was also the 'referring court' mentioned in the case - it referred some issue to the EPA (a department/commission/agency, not a court) to implement or decide, and is now hearing the review - so in this case the reviewing court, referring court and appeal court are all the same court.
As I found in the Texas cases I read (and as the extract below shows) usually the reviewing court will be a different court to the referring court - at the same or different level - and the reviewing court may or may not be named an appeal court (although a review is a kind of appeal) depending on it's level and function.
(This is all US terminology for Texas as far as I have made out from the sources - be gentle to me you members of the Texan Bar, out there, - and of course in the UK they name things a bit differently, as Lucy so nicely explains:-)).

http://www.law.emory.edu/1circuit/nov99/98-1036.01a.html

United States Court of Appeals (For the First Circuit)
ASSOCIATION OF INTERNATIONAL AUTOMOBILE MANUFACTURERS,INC (and others) [the Plaintiffs, Appellees(bringing the appeal) versus the EPA (Enviromental protection Agency).

"if the issues referred to the agency . . . are critical to judicial resolution of the underlying dispute, the court cannot proceed with the trial of the case until the agency has resolved those issues. In many circumstances, the court that referred the issues to the agency also must wait until the agency's decision has been either upheld or set aside by a different reviewing court."

"1. It is significant that no proceedings have been initiated in this jurisdiction, by motion in this action or by filing a separate action, to challenge the EPA's September 15, 1999 decision. Therefore, although we precipitated the EPA decision by invoking the primary jurisdiction doctrine, it is at least arguable that the force and effect of the EPA decision are issues not properly before us at this time. See also United States v. General Dynamics Corp., 828 F.2d 1356, 1360 (9th Cir. 1987) (stating that, under particular statute at issue, agency decisions on primary jurisdiction referrals may not be collaterally attacked in proceedings before referring court)."