A button is a fastener that joins two pieces of fabric together by slipping through a loop or by sliding through a buttonhole.
Brass buttons from the uniform of a Danish World War I artillery lieutenant
Modern buttons made from vegetable ivory
Spanish button (approx. 12 mm) from ca. 1650–1675
Button stamping machine at the Henri Jamorski Button Factory in Paris, 1919
A fastener or fastening is a hardware device that mechanically joins or affixes two or more objects together. In general, fasteners are used to create non-permanent joints; that is, joints that can be removed or dismantled without damaging the joining components. Steel fasteners are usually made of stainless steel, carbon steel, or alloy steel.
Typical fasteners (US quarter shown for scale)
Structural bolt DIN 6914 with DIN 6916 washer and UNI 5587 nut