The famous Neo-Confucianist Zhu Xi considered that “Heart” was the cognitive subject and the practice subject, it was the cognitive object that every knowledge including human and all things on earth relations, but the most of all was the principle of morals such as filial piety, righteousness, loyalty and credit. Their relationship was that the cognitive object(every knowledge) was discovered and isolated by the cognitive subject(the wise heart). It can make “heart” and “all things on earth” concordant by exploring rule from thing(即物穷理), and can realize the subject's cognition to object.
Hong Dae-Yong, as one of the representative abandoning Neo-Confucianism scholar, considered that “the practical heart” was the most important cognitive subject, it meant to take the practical matter and article as the object of cognition. Their relationship was that “the practical heart” as the object of cognition reached factual matters and factual articles and realized the subject's cognition to object. That is to say: we should put “the practical heart” into practice and reach cognition about factual matters and factual articles, so that we can innovative applications on reality(经世致用) and use everything to secure a better livelihood for people(利用厚生).
As we can see the differences between Neo-Confucianism and Abandoning Neo-Confucianism from above three aspects content.