There is no formal definition of a "pathway" and the difference between these terms is ill-defined and vauge.
A network is any structure which has nodes that are connected by edges. Usually we talk about genes/proteins being nodes, and the edges being some sort of functional relationship. What that relationship is, depends on the network in question. In a protein-protein interaction network, proteins that physically interact are connected, in a co-expression network genes that are expressed at the same time and place are connected. In a regulatory network, genes/proteins are connected to the genes/proteins the mechanistically regulate. In all cases, the assumption is that connected genes/proteins are functionally related.
The concept of a pathway comes from the pre-big data age - from genetics and metabolic biochemistry. The orignal pathways were metabolic pathways, like the glycolytic pathway were enzyme 1 turns meteabolite A into metabolite B, and enzyme 2 turns metabolite B into metabolite C. This was quickly joined by geneticists making pathways from causitive pathways from mutations. And signalling pathways (like the MAPK pathway).
In the end they are more or less two different ways of conceptualising the same thing, depending on the background you come from. Pathways are generally linear, with some branching and cross talk, networks are generally like spiders webs, with many things connected to many others. Pathways are also generally directed - they have a start and an end and infomation/energy/metabolites flow from one end to the other.
Networks are probably a more "accurate" description of what is going on in a cell, with many things connected to many others and information radiating out across the network. But pathways are more intuitive to think about, and don't suffer from the problem that in the end, the whole cell is just one big network, and breaking it down into seperate networks mean putting arbitrary thresholds on things anyway.