The distinction between money and currency is one that is blurry and arbitrary.
No. The distinction between money and currency is quite clear!
Money is the monetary form itself. It is the "thing" we use as money. Its value doesn't depend on a single body or entity safeguarding its value.
Currency is the certificate that certifies you have money kept in a storage somewhere else. It is a storage receipt payable to bearer on demand. The storage owner/keeper has to take care that all issued certificates are backed by adequate quantity of the "thing". In different countries and during different times this certificate was different. It had different properties, attributes, and requisites to avoid dishonest storage owners/keepers and counterfeiting. The latest reliable certificate with most current properties, attributes, and requisites was most widely used for transactions. Hence, the newly coined word "currency" describing current certificate in circulation.
If we use LN we'll be using bitcoin not as money but as currency. Using currency instead of money is riskier but much cheaper. It is a trade-off. People will have a choice depending on their willingness to take small risk in exchange for much lower tx fees. And that is GOOD!
Your are correct of course that there is a huge difference between something secured by a single body and something that is not subject to such counterparty risk but I would again note that your line in the sand here is somewhat arbitrary.
What if you have an asset that is secured not by one body but two or five or 50? Is it money or currency? What we are dealing with here is a spectrum not an absolute. There was a time when pure copper bars based on their weight in copper was money in some countries.
The more distributed your risk is and the less dependent on a single actor the more solid and safe your money/currency is provided it has solid fundamentals and limited supply. Copper as money failed due to eventual oversupply of the metal. Physical ownership of metal has a counterparty risk as well as does bitcoin.
I don't understand what counterparty risk has to do with money/currency distinction? Counterpaty risk is the probability of not getting good or services you have paid for or not getting the money if you're the seller. If I hold a gold coin in my hand or I''m the only one that knows the private keys of a bitcoin address then there is no counterparty risk and I'm 100% confident that I received payment for goods or services I sold.
It doesn't matter how many members one organization has - two or five or 50. You have to define what do you mean by "secured by"? I'm using "depends on". Doesn't depend on means if that organization of two or five or 50 members disappears this asset was and still is money if it still has value. If the value of this asset goes to zero then it was currency before losing its value as it was backed by a second asset that disappeared. The distinction is very clear. If something is backed by nothing and is used as money then it is money!
Until 1971 the US dollar was currency. It was a certificate giving you the right to convert it into gold as it was pegged to gold. After gold window was closed the US dollar became money. Yes, that's right! If you present a 100 dollar bill to the Fed they will not redeem it as they don't have any obligation whatsoever. If Fed disappears the US dollar will still have value IF it is scarce and has limited supply! I'd even say that without Fed the value of US dollar will increase.