Is there any difference in meaning between "die Ordnung" and "die Reihenfolge"? They both seem to mean order, but I'm not sure when to use one over the other.
"Reihenfolge" is used when you want to express that one thing comes after the other other in a certain way.
"Die Reihenfolge der Bearbeitung ist folgendermaßen ..." means "The order of processing is as follows ..."
"Ordnung" can be used as a synonym. Not sure if it would suit everywhere. "Die Ordnung der Bearbeitung ist folgendermaßen ..." would sound strange to me. Although I would understand what's meant.
"Ordnung" is used more generally.
Germans have it in a lot of words and expressions. "Öffentliche Ordnung" for example is the "public order".
"Alles in Ordnung? means "Everything alright?".
Ordnung: generally order in the sense of non-chaos, tidyness, public order
also: taxonomical order (category of species), in mathematics power of a polynomial or order of an approximation
Reihenfolge: order as in a sequence or a queue; order of elements, first, second, third,..
By the way, neither of them is related to the English monastic/knightly order, which would be an (Mönchs- bzw. Ritter-) Orden (Star Wars botched the translation here with its Erste Ordnung).
An order issued by a general also is another meaning - German: Befehl
Just to add something that has not been remarked yet, mathematically, Ordnung can also be used to express the power of a polynomial.
Such as 2n^2 - 1 would be a "Polynom 2. Ordnung".
Scientifically it is commonly used to imply categorization, in general language it is usually used to imply either tidyness (of a room for example) or political stability (as in "Law and Order").
I would say that Ordnung stands for a defined system of sorting. And Reihenfolge is a defined system of counting, where a sequence of object is considered.
Intuitively I would say Reihenfolge is something one-dimensional, similar to a recursion or a simple mathematical sequence. Ordnung can be more abstract, it could mean the particular position of molecules or the state of a database.
Maybe one could argue that a Reihenfolge is one element of the set of all Ordnung, while the contrary does not hold.