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.
Cryptocurrency is not a real store of value, though. It is basically at the same level as fiat on Exter's pyramid. Wealth is derived from resources and labor. Cryptocurrency will always be the bad money driving out good money compared to an actual resource/commodity based currency whether it's gold, silver, oil, or some other substance. The problem that it's very difficult to remove counterparty risk on things like uranium and oil always switch roles back to metals such as gold and silver instead.
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The difference is that cryptocurrency has the potential to someday climb beyond fiat beyond gold even on Exter's pyramid.
Gold can essentially be thought of as an eternal partially anonymous POW blockchain. It is mined and mining requires work limiting its supply and allowing it to be used as a store of value. Gold does have counterparty risk. The counterparty is society. The purchaser of gold takes the risk that the gold network (the network of individuals in society willing to buy and own gold) will continue to exist. Governments play a role here in that they have the power through their actions to strengthen or weaken this network but they lack the ability to destroy it entirely. The gold network has existed for thousands of years it has also survived multiple government attempts to eliminate it so the counterparty risk is lower than with anything else that exists.
To displace gold cryptocurrency would need to have a counterparty risk that was lower than gold.
This would require
A) Demonstration of enternal nature currency would need to hold its value over several generations
B) Demonstration of resilience cryptocurrency network it would need to show its ability to survive outlast and not be broken or destroyed by hostile government action.
The jury is still out on whether bitcoin can meet these very high hurdles. However, even if bitcoin fails it seems almost inevitable that something will come along someday that can meet them.