No, the term "natural order" is not specific to Java. My opinion is that it does not apply to programming languages at all; rather, all programming languages (although they may or may not use the term explicitly) rely on the concept.
For example, how does a method like max(a, b) or a.after(b) if the concept of natural ordering does not exist? We know the natural order of integers: 1, 2, 3, ...; dates 1/1/1990, 1/2/1990, 1/1/1991, ...; time: 12:00, 12:01, 1:01 ... These systems are defined by man, but this is what we expect. If we had integers ordered 1, 3, 2, 4, that would be unnatural.
Your quote, as I read it, offers exactly that. A type that implements the Comparable interface provides a “standard”, well-defined, or expected order. For types defined by developers, the developer must provide natural ordering (as Java developers did with Numbers) or define the natural order, as we often do with complex types.
When a class implements the Comparable interface, it provides an orderly (natural) change-only ordering, providing a custom Comparator . However, there is a limited number of objects or systems that we can represent in software that has a true, well-understood and accepted natural order. Many types, such as students, cars, and users, may depend on one or a combination of attributes that determine their order, which may seem natural at all.