You may not call checkbook money "money", but it's 90% of what most people and industry needs for commerce. Some countries are exploring eliminating paper money altogether. Base money will then just be numbers in checkbooks between the fed and the banks. That will certainly "confuse" normal people.
No, checkbook money are just like your bitcoins in an exchange, it is the number that platform shows you, just a number in their database. It is this part most of the people misunderstand
For example, you put 100 bitcoins in an exchange, your account shows a number of 100, exchange write 100 coins in their checkbook. However, those coins went to their own wallet, and get moved to somewhere else. You still play around with the platform thinking you are playing with your bitcoin. But one day, the platform closed and the owner claim it was hacked... In fact, those coins are long gone the moment you put them in, you were just playing with numbers in their database
Same for the banks, the moment your 100 dollar bill were saved into a bank account, it is gone, you are left with only a number in your account to play with. Banks lend 90% of that bill to another people and he deposited or spent and deposited to merchants account in the same bank and they get another number 90 dollars, and so on. Because there are many people playing in the bank's account just like in an exchange, they are all playing with numbers, it is these numbers banks call it M2 M3 etc... But without your original dollar bill, these numbers will all disappear since they never existed in reality, that is the reason banks strictly restrict your daily withdraw of cash, a large scale of cash withdraw will empty their vault quickly
So, base money is the money, checkbook money is database numbers, just like your bitcoins in an exchange, they never existed in reality
When you do commerce with other people, those numbers move around: Your numbers get lower, merchant number get higher. From bank's point of view, the sum of your numbers does not change, they don't need to move money around, just adjust numbers in your account. However, every time the same money get loaned again, there will be new numbers generated in the database, that is the reason they say loan create money, in fact it only create new database numbers
If paper money is totally eliminated, then the loop will close, banks will never have a bank run and can create as much money as they want to rob people of their wealth. But what if people abandon their money altogether and don't play with their game anymore? Bitcoin fist time in human history let you hold your own money without the need to put them in a bank and play with numbers in their database, this is a vast evolution