Liquor is simply the common name for any distilled beverage. To become a liqueur, a base liquor (i.e. grain spirit, brandy, rum) is sweetened with the addition of fruits, flowers, plants, or pure juices to achieve a minimum sugar content of 2.5%. This infusion of sweetness and flavor is the primary factor that makes the two categories so distinct.
Though you will often see flavored liquors, these flavors are added rather than infused, further separating them from liqueurs. Both categories can be of equal potency, with some liqueurs going as high as 110 proof. Therefore, alcohol percentage is not a distinguishing factor.
Cordial is another name for a liqueur, so keep that in mind to reduce confusion!