This relationship of meronymy is controversial for various reasons. First, there are several types of meronymy, such as functional meronymy, where one concept is a functional part of another (e.g. FINGER-HAND) or more general part-whole relations, where the part and the whole exist as a continuous entity (e.g. FLAME-FIRE). Secondly, there are diverging opinions as to whether meronymy should be treated as a semantic primitive in the sense of s[yn]onymy, antonymy, and hyponymy.
Source: wiktionary
But whereas hyponymy is a member–class relation, reflecting a taxonomy or conceptual hierarchy, meronymy is a part–whole relation, reflecting the existence of complex structures in concrete reality.
Source: wiktionary
Possession, like meronymy, is described in English (and equivalently in other languages) with the verb to have (A millionaire has money) and the line between possession and part-having is fuzzy at best.[…]Priss (1998) suggests that meronymy might be formalized as an attribution relation, such that has-a-handle-for-a-part would be an attribute of hammer and cup. Thus, the case for separating attribution and possession from meronymy is not strong.
Source: wiktionary