You might be referring to Pyracantha. They are large, thorny shrubs that have white flowers in May and June and are dotted with red, orange or yellow berries in autumn.
Elderberry Bush
Holly
The most likely red berries around Christmas are on holly plants (Ilex aquifolium).
Strawberry Bush -Euonymus Americanis
A Holly Bush.
Holly Bush/ Ilex
Roses, prickly pear cacti, Jumping cactus (cholla)
a holly bush has shiny green leaves that have sharp points and red berries.
The name of a red vined thorn bush is "red vined thorn bush."
Might be a holly bush leaf but im not 100% sure :)
The male holly bush fertilizes the female holly bush... thus causing the female holly to produce the red berries
Red