hard to say, and the r many people use is nothing like the standard printed version either. I think handwriting and printing have just developed along slightly different tracks. But different fonts do use different letters.
It would be interesting to ask about people's handwriting styles. I use italics when using my italic nib fountain pen but use cursive when writing with a felt tip pen, biro (shudder) or pencil.
I can't point to a source, but I think it goes back to the first days of printing as a way of putting an alignment into each letter to set a straight line of type, giving spacing and a proportional, consistent look to printed words
My handwriting is very distinctive,
I write my lower case a's exactly as they appear here.
I decided in my teens that I wanted to make my handwriting stand out and be different, and I have written this way ever since. X