Common holly: The plants from the Ilex genus are called holly. There are a lot of different versions of its origins, but no matter which language it is derived from, Holly has become the name particularly used for Ilex genus. As this plant is the most common plant in the genus, it is called common holly.
Christmas holly: Its glossy green and prickly leaves and bright red berries (produced only by the female plant) are represented in wreaths, garlands, and cards wherever Christmas is celebrated. So, it is called Christmas Holly.