If everyone agreed on a single volatility, every option on a coin would have the same IV. They don't, and the differences are one of the most useful things the options market tells you.
Skew: which way the market is afraid
Compare the IV of puts and calls the same distance from the money, usually at 25 delta. When puts are dearer, traders are paying up for protection against falls. When calls are dearer, they're reaching for upside. The conventions differ: a "risk reversal" is often quoted as call IV minus put IV, while "put skew" means the reverse, so always check the sign before you read the number.
Term structure: when the market is afraid
Plot IV by expiry. Longer-dated options usually carry higher IV, a shape called contango. When short-dated IV jumps above long-dated, the curve inverts, usually because the market expects trouble soon or something big has just happened. It tends to come back to normal once the moment passes.
Put them together
A surface maps IV by strike and expiry at once. Rich short-dated puts with a calm back end say something quite different from rich long-dated calls, even when the headline volatility is the same.