As has been covered before, a spell or ability is countered on resolution if all of its targets are illegal when the spell tries to resolve. When a spell or ability is countered on resolution, no part of it will resolve. For example, if the target of a Slice in Twain is removed from the battlefield before it resolves, the Slice in Twain will be countered on resolution and the controller of the Slice in Twain will not draw a card.

Sometimes a spell or ability requires more than one target in order to perform an action when it resolves. For example, Puca’s Mischief‘s triggered ability targets two different non-land permanents. Technically speaking this ability will still resolve if one of these targets is not legal when it attempts to resolves, however because of how this ability works nothing will happen as the exchange cannot take place.

Compare this to what happens when Aura Finesse resolves. If just one of the targets of Aura Fineese is not legal when it attempts to resolve, then this first action cannot be performed. However, as this spell is still resolving, the controller of Aura Finesse will still draw a card. In order for Aura Finesse to become countered on resolution both the targeted aura and creature would have to be illegal targets when Aura Finesse resolved. In this instance, the controller would not draw a card.