Calligraphers hand-draw letters using a pen, brush, or other writing instruments with the focus on skilled reproduction of established forms called calligraphy alphabets. Distinct from lettering and typefaces.
character
A character is a mark—letter, number, punctuation, technical symbol, etc.—used to convey meaning in written text. It is the smallest functional unit of a writing system.
lettering
Artists illustrate a specific word or phrase for a single applications like a book cover, sign, or article graphic. Drawn from scratch and includes only the illustrated letters. Distinct from calligraphy and typefaces.
scripts
The set of characters used to represent a written language. There are 294 known writing systems, but not all writing systems have been deciphered. A single writing system (like Latin) can be used for many different languages, and a single language (like Japanese or Sanskrit) can be written in more than one script. 131 scripts have yet to be encoded in Unicode. The most common scripts include Latin, Chinese, Arabic, Devanagari (used for Sanskrit, Hindi, and other Indian languages), and Bengali (used for eastern Indian and South Asian languages). Others include Greek, Cyrillic, Armenian, Hebrew, and Georgian scripts. See Missing Scripts Project’s World Writing Systems for a list of the 294 known writing systems: https://www.worldswritingsystems.org/ See Scriptsource’s glossary for terms related to writing systems https://scriptsource.org/cms/scripts/page.php?item_id=glossary
Note: alphabet and script are not synonymous terms. A script can based on an alphabet (alphabetic), logogram (logographic), or syllable (sysyllabic), among others.
typefaces
Type designers create a complete alphabet designed to work as a modular system for an infinite number of applications. Distinct from calligraphy and lettering.