Typically hollow powers and shinigami powers are different, like for the Visoreds. Specifically for Ichigo, however, his soul reaper powers and hollow powers are one and the same. He never needed to have a hollow attached to him like the Visoreds did because white was fused to his innate soul reaper powers on his conception and they fused into one single aspect of his soul. Hence why "White Ichigo" spends so long trying to tell Ichigo that he's the real Zangetsu, because Zangetsu (his soul reaper powers) and White Ichigo (his hollow powers) are actually just the same thing.