To put it maybe a bit too simply, MZT is Marxism-Leninism adopted to mid-century Chinese conditions, whereas Maoism is a branch of ultra adventurism. From my understanding of the history, it kicked off around the time Deng became Premier and started to implement the policies that comprised Reform and Opening Up, as an ultra-left reaction against these policies.
Maoists think that Deng took the Capitalist Road. Students of MZT can see the thread connecting classical Marxism, Leninism, MZT, and modern SWCC and recognize that they all play their part in building communism in China.