- Design System

- Styleguide

- Living Styleguide

- Component Library

- patternplate

Design System

A coherent set of principles, constraints and rules describing how to design inside a given system.

Also: Design Language

Example: Google Material Design

Source: What is a Design System?

Styleguide

Document describing a design system, explaining its rules with concrete examples. Often employs a "Dos and Don'ts" schema.

Also: CI Guide

Living Styleguide

HTML version of a Styleguide.

Includes and documents live code examples alongside relevant rules. 

Component Library

Technical implementation of all frontend components needed to create websites and applications that should feel and look alike. Often is a the result of a project also using a Living Styleguide.

patternplate

An OpenSource software to create Living Styleguides and Component Libraries efficiently. It provides a ready-made Web interface to display Living Styleguide contents alongside an automatic listing of component in the documented component library