Does the terminology "contested" when applied to a case under appeal, mean simply that the defendant is appealing the the appeal, or does it mean something different?
An appeal may be made by a plaintiff, prosecutor, defendant or other interested party, so the term 'defendant' is not very useful; the party opposed to the Appellant (and served with the appeal) is usually called the Respondent.
A contested appeal just means that the Respondent wishes to be represented at the appeal, presumably to fight it; most appeals are contested, but not all. Unlike a first-order case which may go by default, an uncontested appeal will still have to have some sort of a hearing; you are, after all, saying that a court decision should be set aside, and the Respondent's views are not necessarily relevant. It is, though, fair to say that an uncontested appeal will have a greater chance of success.
A "contested" appeal does not mean that "the defendant is appealing the the appeal[.]"
Usually an appeal is considered "contested" if an answer brief arguing that some or all of the relief sought on appeal should not be granted is timely filed in response to the opening brief on appeal filed by the party filing the appeal.
The fact that an answer brief is not filed in an appeal does not mean that the party filing the appeal automatically wins (as would be the case in a civil action in the trial court where the defendant failed to file an answer), but gives rise to a more lenient standard of review than in a contested appeal.
There are also very rare cases where an answer brief is filed and the answer brief concedes that the appellate court should rule in favor of the appealing party on all issues presented.
For example, Denver recently had a change in District Attorney since the old District Attorney was term limited. There was one case of which I am aware in which the defendant appealed a sentence after the old District Attorney had argued that the sentence as valid in the trial court, prevailed in the trial court, and caused the defendant to appeal the sentence. But, the new DA disagreed with the legal analysis and/or position taken in the case by the old DA and the trial judge, and concluded that the sentence was invalid and that she would lose on appeal (the issue concerned the application of a recidivist sentencing statute in Colorado to cause a minor offense to have a very long sentence). So, the new DA filed something in the appellate court conceding that the defendant should win and the defendant's appeal was granted summarily.
But, the second scenario is normally not what someone is talking about when distinguishing an appeal that is contested from one that is not contested, even though, in theory, neither scenario is a "contested appeal".