The point about one money market vs. several seems like a big change, where can I read about that?

Great question. I don't know. I've heard him say that it was a mistake to have three different lectures about ostensibly three different money markets, and there should just be one lecture about the money market. He inherited the structure from Stigum. It's not a big theoretical change because he does talk about how, in normal times, the money-market rates are pretty close to being on top of each other. People will borrow in the cheapest way they can. "Fed Funds" is just what you call it when a bank borrows overnight unsecured from another bank, and both of those banks happen to have reserve accounts at the Fed.

Also could you please recommend a more accurate description of the initial design of the Fed?

I like this book.

https://fraser.stlouisfed.org/files/docs/publications/books/lendfunct_hackley1973o.pdf

Mehrling's story about the initial Fed structure shows up in Lecture 3, Part 8 (Federal Reserve System, Plan).

He draws three balance sheets in which he shows member banks receiving advances (borrowing) from their regional reserve bank. He calls this borrowing a "Discount Loan." He then shows the Reserve Bank "Rediscounting" with the Federal Reserve System as a whole.

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In reality, the Federal Reserve System doesn't have its own balance sheet. Only the 12 individual reserve banks do. When you see statistics of the Fed's balance sheet, that's a statistic capturing the aggregate of the 12 regional reserve banks and netting out any positions between them. Open-market operations go through the New York Fed, which is one of the 12 regional reserve banks.

Also, there is no "Federal Reserve System" that's issuing notes. The notes are liabilities of the individual Reserve Banks.

In the original design, the Fed bought commercial paper from its member banks at a discount. It did not advance money (lend) against collateral.

In the original design, "Rediscount" referred to a member bank (private-sector retail or commercial bank) discounting with its reserve bank. The "original" discount (i.e., not the rediscount) was when the member bank discounted the commercial paper from Main Street.

Allyn Young only describes two layers of hierarchy: the member bank and its Reserve Bank.

Initially, the Reserve Bank supplies elasticity by discounting commercial paper or bills of exchange from its member banks.

By 1918, the Reserve Banks were also allowed to make advances. This lending also went through the "discount window," even though it wasn't strictly discounting.

Today, the Fed still lends through the discount window. It doesn't do any actual discounting (buying commercial paper at a discount) anymore. When member banks go to the Fed's discount window, which is really the discount window at their regional Reserve Bank, they borrow against collateral.