No. All plums are members of the Prunus genus, which is also home to apricots, peaches, almonds, nectarines and cherries. They belong to the Rosaceae (rose) family. Citrus fruits, on the other hand, belong to the Citrus genus, which is part of the Rutaceae (rue) family.
Common purple plums are known as Prunus domestica in Latin. They came to the United States from Europe, but probably originated in southwestern Asia. Prunus domestica has also been hybridized with Prunus salicina, which is the Japanese or Asian plum. Members of this Asian species have reddish skin, and the hybrids appear somewhat purple.
The Citrus genus is home to lemons, limes, grapefruits and tangerines. Citrus family members are evergreen shrubs or small trees with prominent thorns or spines. Plants in this genus are native to Asia and the Malay Peninsula. They are not hardy in cold-weather climates.
Commercial plum trees and citrus trees are often grafted specimens, with desirable top growth grafted onto the rootstock of a tougher variety. The two genera both produce trees with attractive blossoms and edible fruits.