Programming is the art and/or science of creating a program, a set of instructions for a computer to do some work.
Software is a mass noun for programs.
The first computer programmer is widely recognized to be Ada Lovelace, daughter of Anabella and Lord Byron (the poet). Anabella gave her love of mathematics to Ada, who after meeting Charles Babbage, translated and expanded a description of his analytical engine. Even though Babbage never completed construction of any of his machines, the work that he and Ada did on them earned her the title of the world's first computer programmer.
Programmers often refer to programming as coding. However, they don't like to be treated as mere coders.