Does a Change in Implied Volatility Affect At-the-Money and Out-of-the-Money Options Differently?

Yes, changes in implied volatility have a different impact depending on an option's 'moneyness'. At-the-money (ATM) options, where the strike price is very close to the current asset price, are the most sensitive to changes in implied volatility and thus have the highest vega.

Out-of-the-money (OTM) and in-the-money (ITM) options are less sensitive. This is because the value of an ATM option is almost entirely extrinsic value (time and volatility value), while the value of deep ITM or OTM options is more dependent on intrinsic value or the low probability of becoming profitable.