Handwriting is the act of writing by the human hand, usually with a pen or pencil, in a casual manner (unlike the decorative nature of calligraphy or lettering). “Handwriting” or “handwritten” may also refer to a loose genre classification of typefaces: those resembling a handwritten style.
Note that there’s a large crossover between the “handwriting” and “script” genres of typeface classification. Examples of handwritten typefaces include Kalam and Tillana.