Proteins interact with each other often for regulation purposes and for localization of several enzymatic reactions for increased efficiency. For example, some proteins inhibit their binding partners. Or DNA replication complex is made of bunch of proteins, many of which do different jobs, but they are in physical complex (e.g. helicase with DNA polymerase).
Metabolic networks are sets of chemical reactions, they might even happen in different compartments inside the cell. While you can try to investigate protein interaction network by cross-linking proteins and then analyzing complexes you extract, metabolic networks are constructed by deciphering sequences of chemical reactions (e.g. metabolic cycles) and finding appropriate enzymes for each reaction.
Metabolic process (e.g. DNA replication) can be run by interacting proteins, but also might include proteins that don't directly interact with each other. For example, DNA polymerase complex does not produce nucleotides, but they are necessary for it's function.