The benefits that McDonals generate dont go to the government. McDonals pays taxes.
The government gets the same benefit from McDonalds that they get from the Federal Reserve. They get a product that they can buy.
Whether that is hamburgers for Congress or dollars for the US Mint. They are both products, paid for by the government to private entities.
No, legally they are different things. And in real life they are quite different as well.
A corporation in the USA pays as taxes a percentage of their benefits. The USA has one of the highest corporate rate in the world (the first or the second if I recall correctly) and it is something over 20%. The Federal Reserve gives their benefits to the government. There is a big difference.
Also, the Fed is not private. Mcdonal is.