The phrases "the metal of a frying pan" and "of metal frying pan" have slightly different meanings due to their word order and usage.
"The metal of a frying pan": This phrase refers to the material or composition of the frying pan. It implies that you are specifically referring to the metal component of a frying pan and not other aspects like the handle or coating. It focuses on the material from which the pan is made.
"Of metal frying pan": This phrase is not commonly used in English and may be considered grammatically incorrect. However, if we assume you meant to say "a frying pan made of metal," the meaning is similar to the first phrase. It implies that the frying pan is constructed using metal as its primary material.
In both cases, the emphasis is on the fact that the frying pan is made of metal. However, the first phrase ("the metal of a frying pan") focuses on the specific material, while the second phrase ("a frying pan made of metal") describes the pan's construction using metal.