Christmasberry (Christmas berry, Christmas-berry) can refer to any one of several shrubs or small trees, as well as their colorful fruit:
Ardisia crenata, native to Asia and Australia
Crossopetalum ilicifolium
Lycium carolinianum (Carolina Desert-thorn, family Solanaceae), a boxthorn native to subtropical North America
Heteromeles arbutifolia (Toyon or California Holly, family Rosaceae), native to southern California and northern Mexico
Passerina ericoides, a South African shrub
Photinia villosa
Ruscus aculeatus cultivar 'Christmas Berry'
Schinus terebinthifolius (Brazilian Pepper, family Anacardiaceae), native to South America but introduced and invasive in many tropical and subtropical areas