>> Interpreting "printing money" to replace the more technical "controlling the size of the monetary base[1]"
These are different things.
Printed money is cash (or currency) and it represents a small amount of the total money in use, just under 3% in the UK. I don't have the figure to hand for the US but it's comparable, less than an order of magnitude difference. Printing money isn't a significant driver of the size of the monetary base, currency is (more or less) printed to replace the notes & coins that are guessed to have been lost or damaged. Talk about printing money, especially as a means to expand the monetary base, is usually misguided.
The monetary base consists of currency in circulation + reserve balances.
Reserve balances in the US, since March 2020 (Fed reserve requirements changed to 0%), refers only to the balance recorded in the account at the central bank for a given commerical bank (or other approved user of reserves). Reserves are money but they're a special kind of money that can't be spent in the economy. They're only usable by the central bank and institutions who are licenced to hold reserves at the central bank (predominantly commercial banks). They're not phyiscal (reserves used to include actual cash in the vault back when there were reserve requirements). Reserves, like most money today, just exist as rows in a DB on a computer.
There's an unlimited supply of reserves available to commercial banks (via the discount window), they are created on demand as needed from nothing by the central bank and charged at the discount rate in unlimited supply. A commercial bank today cannot run out of reserves.
>> the fed tries to tweak the money supply
The fed doesn't control much of the money supply, most of our money is created as commercial banks issue new loans. There's a common misunderstanding that commercial banks operate as intermediaries lending deposits, but they don't.