aglet

The cover at the tip of a shoelace, to prevent it from fraying.

A catkin.

A tip, originally of metal and often decorative, on a ribbon or cord that makes lacing two parts of a garment or garments together easier, as in corset lacings, "points" (lacing hose or trousers to jacket or doublet) or sleeves to a bodice.

An ornament worn on clothing, consisting of a metal tag on a fringe, or a small metallic plate or spangle.