A food chain is a linear sequence that involves links in a food web starting off with a producer (like a plant), primary consumer (herbivore), Secondary consumer and tertiary consumer. So it is this link that involves one organism eating another organism and so on.
A food web, however, is the natural connection of food chains through a graphical representation of what organism eats what in an ecological community. This is different to a food chain because, in a food web, a particular organism has the probability of being eaten/eat more than just one organism.
(Source, Difference btw, 2015)