Dictionary.com has it as "to arrange according to sort, kind, or class; separate into sorts; classify". I looked it up in the OED too -- mostly because we have one and I don't get enough excuses to use its nifty little magnifying glass -- and it also supports the notion that it means by category, not by order. The general verb definition is "to arrange things according to kind or quality", and there's a separate definition for software: "sort: Computers: the action of arranging items of data in a prescribed sequence".

I think I've always thought of ordering as a subset of sorting, not something different, both in computing and in "real life" language use.

When sorting washed laundry I categorise by type and order by a fairly arbitrary mix of target position (undies in the top left draw, socks top right, daily t-shirts the draw below, "better" t-shirts the draw below that, then trousers, ...), hue/pattern/subject, and a few other properties. As with your cards example there are both grouping and ordering operations present in the sorting operation (in the cards example there might be two orderings: one for the suits if you want them to be in a specific order and one by the value of the cards within the suit).

Sorting numbers in a computer seem quite different: each category has at most one item and the are ordered by the same property they are categorised by, but the process is similar enough.

And sorting in computing is not always simply ordering. There are many examples where it is categorising (just by some variety of ordinal value). Some sorting algorithms explicitly categorise the input data as a divide-and-conquer process. Sometimes you don't care about the precise ordering (but it is done precisely anyway because a fuzzy sort would be no more performant).

The only examples that immediately jumps to mind where there is a definite distinction made are data management languages where there is a distinction between ordering and grouping (quite explicitly seen in SQL's "order by" and "group by" clauses), and even there I know that internally ordering/grouping/both are performed by what I would identify as a sort operation.

Sorting doesn't mean something different in computing really, people just tend to pick out a more specific definition in that context.

If I was sorting lego blocks I don't know if I would do it first by color and then by size/shape (here are all the 2x8s, here are all the 1x4s, etc.), but it would definitely be by category.

size/shape is far more useful.

Go ask your wife how she sorts the laundry.

Most languages are context sensitives, but generalized computing is fundamentally defined by a context free language in which a processing transition can execute and not care was previous states were. This gets blurry with recursion and generics and other syntactic sugar, but fundamentally state changes are still defined by the operation and instantaneous state and not the language itself.

So in our context-free language of generalized computers, sorting and ordering are the same.

What on Earth do you mean when you say “generalized computing is fundamentally defined by a context free language in which a processing transition can execute and not care was previous states were”?

Perhaps you are just writing context free/sensitive when you mean something different from “the set of words that may be formed by starting with some nonterminal symbol S, following rules of the form A -> xy where A is any nonterminal and x and y are either terminal or nonterminal symbols, repeating until there are no nonterminals left.”

If you really mean something about all computations being expressible in a context free language then I suppose I would have to agree but I put it to you that a regular language would be sufficient.

The other thing I can’t understand is what this has to do with either the parent or the article?