He's wrong, it's not "basically" the same thing at all.
> Inflation and money supply are tightly correlated.
Historically, they haven't been. Since 1970 the M2 supply has increased like 36X (7% annualized) but the price of goods is only up 7X (3.6% annualized) -- this includes the inflationary period in the 70s and to the peak in the 2020s just to avoid cherry-picking. [1, 2]
Money supply is how much money is floating around, and inflation is a decrease in the purchasing power of money as measured from prices of a representative basket of goods and services over time.
> "Inflation is caused when the money supply in an economy grows at faster rate than the economy’s ability to produce goods and services." - St. Louis Fed
What they're saying is that when the supply and demand of money are in balance prices should remain relatively consistent (MV = PQ) all else being equal - but all else is not equal. You can't distill the value of money down to one sentence from the St. Louis Fed.
Being the reserve currency and having other world economies dollarized means that there is a ton of external demand for US dollars outside the US economy. That increases supply without touching prices. Taxes are inflationary. Supply shocks are massively inflationary. If we run out of oil and everything doubles in price, that's inflationary - and it happens regardless of money supply. That's just a few random things that are completely left out of the above statement.
Most money issuance in the US doesn't come from the Fed, it happens at retail banks when you take out a loan against fractional reserve, and each dollar is backed by the demand to repay that loan. As economic activity increases, so does the demand for loans, and therefore the supply of money. So generally, within some margin, the money supply tracks the economy thereby satisfying the quote.
[1] https://fred.stlouisfed.org/series/M2SL
[2] https://fred.stlouisfed.org/series/CPIAUCSL