> The ICC was formed out of the ICJ
No, it wasn't. In any sense.
It was a permanent successor to ad hoc criminal tribunals like the International Military Tribunal, the International Military Tribunal for the Far East, the International Criminal Tribunal for the Former Yugoslavia, and the International Criminal Tribunal for Rwanda.
> The ICJ came out of the IMT, which was the Nuremburg trials
No, it didn't, it was the UN system's successor to the League of Nations system's Permanent International Court of Justice (the ICJ statute is modelled on that of the PICJ, the PICJ transferred irs assets and archives to the ICJ on its dissolution, the ICJ was headquartered in the Peace Palace that had held the HQ of the PICJ, and the ICJ even adopted the PICJ seal.)
The ICJ—like the PICJ, a court for disputes between nations—was in no respect a successor to International Military Tribunal, which dealt with crimes by individuals (and, indeed had most of its lifespan during that of the ICJ, starting work only a few months before the ICJ.)