How's that different from any Star Trek episode where a crew member goes to the holodeck and instructs the Enterprise's computer to build a program?

It's not inventing a program, it's completing a command using the information stored in its programming, according to the rules set by its programming. It codes because its trained-on terabytes of code that perform task. When you ask for code that does that task it's just retrieving that information and altering it somewhat based on the rules that dictate its response. Unlike humans however, it's not compelled to design a program that does anything without being prompted.