A core is a general term for one of the icosohedral objects obtained from an AI vessel.
Quantum Computer
A quantum computer (QC for short) is an object appearing almost icosohedral, and holds no special effects. It's obtained from the Edgerunner ships, and will sell on Enceladus Prime for 250 000 E$.
Singularity
A singularity appears as a blue icosohedron, and causes EMP effects and gravitational distortions, visible from it's poles. It is harder to capture than a Quantum Computer, but will reward you higher with a sell price of 1 000 000 E$ at Enceladus Prime.