I used the word 'cursive' because Wesley S, who started this thread did. I don't remember it being used when I was in school.
Never heard joined-up-writing either. It was always called handwriting or script.
My personal letters are computer-typed; like Jim Dixon only the envelope addresses are handwritten, but usually print, not script.

More and more talk and video are used in personal communication so emails are decreasing. No writing necessary! No proofing necessary!