IMO rather than talking about ambiguous "inflation", one should be specific about what exactly is being inflated - "monetary inflation", "asset inflation", "price inflation", etc. Monetary inflation occurred when the Fed printed several trillions of dollars back in 2020, asset inflation occurred soon thereafter, and then price inflation took hold throughout 2021 as that new money trickled into consumers' hands.
It doesn't particularly make sense to call the current rising oil price inflation (that would make "inflation" just a synonym for price increases), but the price of energy going up will cause broad price inflation down the line.
Unless I know I'm talking to an economist I use inflation to mean price inflation, because that's what every non economist thinks it means. You are certainly right that it's ambiguous in a technical sense though.
It doesn't particularly make sense to call the current rising oil price inflation (that would make "inflation" just a synonym for price increases), but the price of energy going up will cause broad price inflation down the line.