There really isn't a big difference other than the food web is made up of multiple food chains. A food chain essentially looks at one animal and shows the path it takes to receive its energy. You usually have a producer(plants, etc), a primary consumer that eats the producer (normally an herbivore), a secondary producer that eats the primary consumer (these usually consist of carnivores and omnivores), and then the tertiary consumer that consumes the secondary consumer, finishing with the quaternary consumer that eats the tertiary consumer. The bottom of the chain normally starts with producers that get their energy from the sunlight and shows how each level consumes their energy from the level below them.
A food web takes the chain and shows how multiple animals can consume their energy. For instance, at the top of the chain is the hawk. The hawk can get energy from multiple sources including snakes, squirrels, rodents, and small mammals. The web will show how the energy from these animals flows to the hawk meaning the arrow will be directed towards the hawk in the web. The web shows these interactions for multiple plants and animals in a given environment.