From the looks of it, hypercasual games have extremely simple mechanics, no progression and often no end. Ex: flappy bird, .io games, etc... Advertising are their main revenue source.

Casual games are also simple but they usually feature some kind of progression, with new mechanics being introduced from time to time. For example, with Angry Birds, you unlock new birds as you progress. Candy Crush has different type of candy. In-app purchases are their main revenue source.