As nouns the difference between nucleolus and core

is that nucleolus is a conspicuous, rounded body within the nucleus of a cell while core is the central part of fruit, containing the kernels or seeds.

As a verb core is

to remove the core of an apple or other fruit.

As an acronym CORE is

congress of Racial Equality.

As a proper noun Core is

the birth name of Persephone/Proserpina, the queen of the Underworld/Hades, and goddess of the seasons and of vegetation. She is the daughter of Zeus and Demeter; and the wife of Hades.