What Is the Difference between Volatility Skew and Volatility Smile?

Volatility skew describes a monotonic relationship where implied volatility either consistently increases or decreases as the strike price moves away from the At-the-Money (ATM) strike. A volatility smile is a non-monotonic pattern where IV is higher for both OTM calls and OTM puts compared to the ATM option, forming a U-shape.

In practice, the crypto market often exhibits a "smirk," which is a type of skew where the curve is steeper on the put side.

How Can the Slope of the Futures Curve Be Used to Gauge Market Sentiment?
What Is the Mathematical Relationship between Basis and the Futures Curve Slope?
What Does a Flat Volatility Curve Imply about Market Expectations?
What Is a “Volatility Skew” or “Smile” and What Does It Indicate about Market Sentiment?
What Is the Relationship between the Slope of the Constant Product Curve and the Instantaneous Price of an Asset in an AMM?
What Is the Concept of “Skew” in Relation to the Time Value of ATM Vs OTM Options?
Why Is the Delta of a Deep OTM Option Often More Sensitive to Changes in Vega than an ATM Option?
How Does the Slope of the Futures Curve Indicate Market Expectation?