The external ornament used in heraldry that distinguishes the coat of arms of a Churchman from those of a layman more than any other is the galero. This broad-brimmed and low-crowned hat was originally a pilgrim’s hat and worn primarily when traveling in a cavalcade to shade one’s head from the sun. In heraldry it was seen as a fitting substitute for helm, mantling and crest which were considered too martial for non-combattants like clergy.
A hat originally used only in Roman heraldry and not really catching on in the rest of Europe eventually the galero came to replace the mitre in the arms of prelates since the former was seen as the more “Roman” option. The galero was first bestowed on the Cardinals of the Roman Church by Pope Innocent IV at the First Council of Lyon in 1245. It was the first hat to be distinguished by the use of a specific color (scarlet) and it was also to be adorned with tassels. However, originally the number of tassels was not fixed. There are various examples of cardinals’ coats of arms that show as few as two tassels suspended from the galero (see the arms of St. John Fisher in color below) and as many as seventy-two! (the arms in black and white above are those of Cardinal Ximenes) What marked these coats of arms as those belonging to cardinals was that the galero, cords and tassels were red and nothing else. No one else could use such a red hat except a cardinal regardless of how many tassels were suspended from it.
The number eventually was fixed at thirty (usually depicted as fifteen suspended on either side of the shield in a pyramidal pattern) only in 1832. A system for distinguishing the ranks of other clergy based on the color of the hat, of the cords and the number of the tassels did not come into existence until the Instruction of Pope St. Pius X “Inter Multiplices” in 1905.
So, all these different colored hats, cords and tassels are really a relatively recent innovation in Catholic heraldry.