The process of writing something with a pen or pencil is handwriting. And you can call the way you write your handwriting too. By the time you finish the handwriting of a hundred Christmas cards, your handwriting will probably be illegible.
When you're taking notes or working on your novel, your process can involve typing, dictating, or handwriting — scrawling on a piece of paper with a pen. Your typical style of scrawl is also called your handwriting — it's the script in which you write. Doctors are kind of famous for having terrible handwriting, while elementary school teachers tend to have very tidy, legible handwriting.