Well, both C# and Java use the same pair of names for this, which is why I went for that:

[IComparable.CompareTo](http://msdn.microsoft.com/en-us/library/system.icomparable.compareto.aspx) / [Comparer.Compare](http://msdn.microsoft.com/en-us/library/system.collections.comparer.compare.aspx)

[Comparable.compareTo](http://docs.oracle.com/javase/6/docs/api/java/lang/Comparable.html#compareTo\(T\)) / [Comparator.compare](http://docs.oracle.com/javase/6/docs/api/java/util/Comparator.html#compare\(T, T\))