Technically they're the same, and his SCII bio explains why;
After completing his mountain training with Kuma, Heihachi stopped at a hot-springs resort to recuperate. There he encountered an ancient metallic fragment. According to old picture scrolls, this shard was a piece of the Soul Edge, a notorious sword from medieval Europe. Heihachi grabbed the fragment in excitement and accidentally cut his fingertip.I knew the SC verse was the same as the Tekken verse. ✅After a moment of dizziness passed, Heihachi looked around at his surroundings, a feeling of uneasiness washing over him. He was no longer at the resort. Heihachi was stunned, but nevertheless remained collected.
He wandered around for a while, and eventually came to the conclusion that he was in not modern-day Japan. He had somehow traveled back to ancient times. Apparently, he was in the latter half of the 16th century. Regardless of the situation, Heihachi knew had to find a way to return to his time.
There was a part of him, however, that was trembling with anticipation of what was about to transpire. He knew the history behind the fragment, which was rife with battles between warriors fighting for its possession. And now, he was right in the midst of it all. What better way to test his strength than in a warring era ruled by power? A fighter could not ask for a better challenge.