I really liked this post by JP Koning who calls for us to get rid of the "monetary triumvirate". This is the idea that "money" has three elements as a medium of account, a medium of exchange and a store of value. JP says we should dump the last two and just stick with the first one. If you read closely you'll notice that JP didn't use the term "unit of account" as is more traditionally used when discussing this concept. Instead, he's referring to some specific thing as the medium of account.
Now, in order to be properly nerdy here we need to be more specific. The unit account is just a measuring stick. In the USA the unit of account is Dollars, in Europe it is Euros and in Japan it is Yen. But the medium of account is an item that defines the unit of account. During the gold standard the unit of account was dollars, but those dollars were measured in terms of a quantity of gold. So gold was the medium of account. But now that the gold standard is long gone the concept of a medium of account has become much more muddied because there is no single item with which we define the value of a dollar. Deposits, reserves and physical dollars are all near perfect equivalents 99.99% of the time. In my view, this makes the concept of a medium of account more confusing than it needs to be and potentially useless.
So I arrive at a rather different conclusion than JP. If one is to understand the idea of "money" then the medium of exchange is a superior conceptualization. And I think of money as existing on a scale of moneyness in which items with more moneyness are more suitable as a medium of exchange. In today's system, bank deposits are the dominant medium of exchange because they are the item with which most transactions are settled at the point of sale. Something like physical dollars or gold have a lower level of moneyness because they do not meet the definition of a medium of exchange to the same degree that something like bank deposits do.
But even though JP and I disagree on emphasis we agree on one thing - in a world of moneyness the concept of "money" actually has a lot less meaning than most people would think. While it's useful to understand how different financial assets are used in the monetary system for specific purposes, it's equally important to understand how those items are convertible into one another which gives them all varying degrees of moneyness. And most importantly, we both agree that the monetary triumvirate muddies the waters of "money" unnecessarily.