What's the difference between a calculus and a programming language?
The meaning of the words is not fixed, but I can give you my interpretation.

A calculus is something that we calculate with in the sense of juggling equations (think manipulation of Taylor series or computation of integrals in analysis). A calculus tells us what the rules of manipulation are, but not which ones we should used in a given situation.

A programming language is something that tells us how to calculate. It tells us precisely how to use the rules. We typically let the computer use the rules, as it is much faster. The rules may be non-deterministic, and there may be very good reasons for them being non-deterministic. It may be in the nature of the calculus that it is non-deterministc (think concurrent communicating processes), or fixing a particular strategy may be detrimental to implementation techniques and optimization.

For example, the $\lambda$-calculus is an equational theory. There are expressions and equations telling us when expressions are equal. The equations do not tell us how to apply them, although people usually have hidden agendas and they present the equations so that later on they can derive useful evaluation strategies from them. But in its essence $\lambda$-calculus is a bunch of equations. It is not a programming language.

In contrast, Standard ML is a programming language. It  is given in terms of operational semantics, i.e., rules of computation. There are derived notions of equality (contextual equivalence, observational equivalence, etc.) which we can put on top of it to think of it as a kind of calculus.

Of course, there are often useful connecitons between a calculus and its manifestation as a programming language. Confluent normalization is just one way of passing from the calculus to the programming language (although sadly some people have made it into a religion of sorts). The interplay between calculi and programming languages is important: the programming languages can actually be used, but the calculi explain what the programs are about.

Just to annoy people, let me also state that pretending that there is no difference between a calculus and its operational manifestation sometimes leads to skewed views of programming and mini-religions within the programming community. You may try to guess which language I have in mind. (It's a very cool language!)