When talking about inflation, there's no such thing as "money supply inflation". The term inflation IS clear, you're just choosing to try and redefine it to match your purposes. Inflation is a rise in the price of goods, full stop.
When using the word "inflation" without context is is referring to increased money supply. When using the word "inflation" with regard to prices it is in a different context. The assumed context is what has changed due to the fact that money supply no longer is directly correlated with price increases. When gold and silver were directly debased, prices of goods were directly inflated. If we still used gold/silver currency "inflation" by itself would be synonymous with price increases. We use fiat currencies and the money supply is increased in certain industries or assets and therefore "inflation" has to be defined more clearly. Debasing fiat is not as direct as debasing commodity backed dollars or gold/silver currency.
The article author does a decent job of defining these, but fails to be clear as the writing progresses.
Prices across the board could increase if say the cost to produce and deliver them went up across the board, perhaps because the cost of energy/oil goes up, perhaps due to constrained supply. This isn't inflation and the price increase isn't due to inflation.
Prices across the board could also go up if war breaks out. That's not inflation.
Those types of price increases are due to the supply side. Inflation is due to the demand side and the available dollars chasing the [same amount of] goods.
Price increases and inflation are not the same thing. They are typically related though.
