Free banking is virtually the same as full reserve banking.

The phrase “free banking” is used here as per this Wikipedia definition, which starts “Free banking is a monetary arrangement where banks are free to issue their own paper currency (banknotes) while also subject to no special regulations beyond those applicable to most enterprises.”

Also, under free banking, commercial banks do not need to hold any minimum amount of reserves, nor is there any deposit insurance.

But under that arrangement, anyone is free to stock up on central bank issued notes (e.g. $100 bills or £10 notes) – unless we’re talking about very strict versions of free banking where central banks are almost non-existent. Plus, under free banking, people are free to store money at government run savings banks (if there are any). E.g. in the UK there is “National Savings and Investments”.

But the latter two forms of saving – storing central bank notes and putting money into a government run savings bank  - amount to virtually the same thing as the so called “safe accounts” that are offered under full reserve banking!!

As to the investment accounts offered under full reserve, the normal procedure there is to have depositors who want their money loaned out by their bank buy into a mutual fund (“unit trust” in UK parlance). And the value of stakes in those funds varies with the value of the underlying assets, just as in any normal mutual fund / unit trust.

In contrast, under free banking, banks can promise depositors they’ll get their money back despite risks having been taken with that money: i.e. that money is loaned on. So the stakes that depositors have in a “free banking bank” is more in the nature of a bond rather than a share. That is, in the case of shares, the price of the share varies day by day and hour by hour. In contrast, in the case of bonds, the value is fixed in that assuming the relevant bank (or non-bank corporation) does not go bust, those investing in bonds ultimately get $X back for every $X they initially put in. 

But as just intimated, those “bond holders” know perfectly well that the value of their “bonds” can collapse to nothing. So to that extent, those bonds are not all that much different to shares or the stakes that depositors would have in mutual funds under full reserve. Indeed, in the US in the 1920s and early 30s prior to the introduction of deposit insurance, about a third of all deposits went up in smoke according to Irving Fisher. 

So all in all, what’s the difference between full reserve banking and free banking? Not much!!!!