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J and K are different languages. They are similar in that both use standard ascii keys and are in the APL family of languages. The author of K "Arthur Whitney" wrote part of a prototype with Roger Hui for the J interpreter or so I think. The primary author of J is none other than Ken Iverson (the Turing award winner and designer of the original APL) who wanted a free version of APL for the masses where people wouldn't complain about the weird non ASCII APL symbols. It also primarily uses a tacit function train style of programming like data flow languages where you don't even necessarily need variables (pretty cool). This tacit coding style has since been added to Dyalog APL where you can see folks like Aaron Hsu build some pretty cool applications using it. I'd imagine K is more performant though than J and the source is famously small (just a few C files). J has a lot more stuff baked in like Qt support. They both have a database library Jd (for J) and Kdb+ (for K). Kdb+ is a fancy SSD based database which uses K and a SQL like DSL called Q. Its performance is pretty darn good and used in Finance. I don't know enough about Jd.

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V1(iota) { // Define one-arg function iota. I n = *w->p; // Get the value of the ω argument. A z = ga(0, 1, &n); // Allocate output array. DO(n, z->p[i] = i); // Assign increasing integers. R z; // Return the result. }

V2(plus) { // Define two-arg function plus. I r = w->r, // Get the rank of ω. *d = w->d, // Get a pointer to ω's data. n = tr(r,d); // Get tne size of ω's data. A z = ga(0, r, d); // Allocate output array. DO(n, z->p[i] = a->p[i] + w->p[i]); // Add corresponding values of α and ω R z; // Return the result. }