While a mullet may have any number of points, it is presumed to have five unless otherwise specified in the blazon, and pierced mullets are common; estoiles, however, are presumed to have six rays and (as of 1909) had not been found pierced. In Scottish heraldry, an estoile is the same as in English heraldry, but it has been said that mullet refers only to a mullet pierced (also called a spur revel), while one that is not pierced is called a star.
The use of the word star in blazons, and how that charge appears in coat armory, varies from one jurisdiction to another. In Scots heraldry, both star and mullet interchangeably mean a star with five straight rays; the official record from 1673 gives Murray of Ochtertyre azur three Starrs argent ... (Public Register, vol 1 p 188), while the Ordinary of Arms produced by a late 19th century Lyon King of Arms 'modernizes' the original as Az. three mullets arg. .... In Canadian heraldry the usual term is mullet, but there is also the occasional six-pointed star (e.g. in Vol. IV, at p. 274 and in online version of the Canadian Public Register), which is what others would blazon as a six-pointed mullet. The United States Army Institute of Heraldry, the official heraldic authority in the United States, uses the term mullet in its blazons, but elsewhere, as in US government documents describing the flag of the United States and the Great Seal of the United States, the term star is constantly used, and these nearly always appear with five straight-sided points.
The term mullet or molet refers to a star with straight sides, typically having five or six points, but may have any number of points specified in the blazon. If the number of points is not specified, five points are presumed in Gallo-British heraldry, and six points are presumed in German-Nordic heraldry.
Unlike estoiles, mullets have straight (rather than wavy) rays and may have originally represented the rowel of a spur, rather than a celestial star. The term is said to be derived from French molette, a spur-rowel, although it was in use in heraldry even before rowel spurs.
The term estoile refers to wavy-sided stars, usually of six points, though they may also be blazoned with a different number of points, often eight (e.g. "Portsmouth County Council" pictured here), and many variants feature alternating straight and wavy rays (e.g. "Honford" pictured here). The term derives from Old French estoile 'star', in reference to a celestial star (cf. Modern French étoile), from Latin stella 'star'.