We learn this from the text of the Kiddush: "And You gave us, Hashem our God, with love, festivals for joy, holidays and times for gladness." These two expressions appear in many places in the texts of prayers and blessings, such as: "Joy for Your land and gladness for Your city" (the Amidah prayer of the Yamim Noraim), "Rejoicing in their going out and glad in their coming in" (the Yotzer Or blessing of Shabbos), "The voice of gladness and the voice of joy" (the Sheva Brachot), and many similar instances. Certainly, both expressions are related to happiness, and it requires explanation what the term "gladness" adds to the term "joy."