What is the difference between DNA pol 3 core and holoenzyme?

Essentially there is not an answer. There are two different definitions.

A holoenzyme is an enzyme that needs to be together with a cofactor (s), required for activity.

In some cases, enzymes constituted by several subunits (like DNA polymerase 3) are call holoenzyme as well, because it will only perform correctly when all its subunits are present.