Comparer extensions take a "source" comparer and apply some additional logic, returning a "result" comparer.

Reverse reverses the comparison used by the source comparer.

var ints = Enumerable.Range(0, 5).ToList(); // [0, 1, 2, 3, 4]
ints.Sort(Compare<int>.Default().Reverse()); // [4, 3, 2, 1, 0]

There is no notion of "reverse" for equality comparers.

ThenBy returns a CompoundComparer. A CompoundComparer always applies the source comparer first. If the source comparer indicates both items are equal, then another comparer is used as a "tie breaker".

For equality comparers, use ThenEquateBy. There is no notion of "descending" for equality comparers.

Sequence converts an IComparer<T> into an IComparer<IEnumerable<T>> by using lexicographical sorting.

For equality comparers, use EquateSequence.