Unfortunately I have to agree that you don't seem particularly qualified.
First of all, "coining money" is not a "right" but a "power". No one has the right to coin money. Specifically, it is the power to stamp a piece of metal with your seal or face or whatever, distribute the coin to others, and yet still claim ownership of the metal. This is the reason the US may also "regulate the value thereof".
They own it. In any other case this would be considered an act of fraud and unjust force. However, since this power was granted to the US federal government by the states, through the Constitution, it is collectively tolerated. And the
reason this power was granted to the federal government exclusively was primarily to prevent sovereign states from melting down each others' coins, as well as to provide individuals with a unit of exchange with a recognizable standard of weight and quality:
COIN, n. Pieces of gold, silver, or other metal, fashioned into a prescribed shape, weight, and degree of fineness, and stamped, by authority of government, with certain marks and devices, and put into circulation as money at a fixed value, Com. v. Gallagher, 16 Gray, Mass., 240; Latham v. U.S., 1 Ct.Cl. 150; Borie v. Trott, 5 Phila., Pa., 403
Furthermore, coin, money, and currency at least (of the terms you listed) each have distinct definitions that pre-date any US government: (emphasis mine)
Strictly speaking, coin differs from money, as the species differs from the genus. Money is any matter, whether metal, paper, beads, shells, etc., which has currency as a medium in commerce. Coin is a particular species, always made of metal, and struck according to a certain process called "coinage." Wharton.
Coin is just one type of money. Money is that which has currency. Currency is
current value. Pop Tarts constitute currency in some places. There is absolutely no reason not to refer to Bitcoins as
currency.
Frankly, your advice to avoid these well-defined terms in favor of more vague ones recently-coined by some three-letter agency is laughably bad. The fact that you do so behind an anonymous account with a Simpsons avatar makes me seriously question your motives.