How is job costing different from activity-based costing?

Those aren't in opposition to each other. i.e. it's not job costing versus activity-based costing.

There's job costing versus process costing.

Activity-based costing is a method of allocating indirect costs versus traditional costing methods that lump all indirect costs together.

Since it's not job costing versus activity-based, I'm not sure what it is that you really need to know. Since you generally will learn activity-based costing after you learn job & process costing, I can sort of assume that if you're asking about ABC costing that you've run across it and that that's what you're really wanting to know about. But this is of course just an assumption.

Traditional costing takes all indirect costs (i.e. overhead) and just lumps them together and allocates based on one cost driver. For instance, based on machine hours. Activity based costing splits activities apart by type and allocates costs based on a cost driver that is appropriate for that type of cost. For instance, electricity would not be caused by human labor, and therefore using direct labor hours to allocate that cost would not make sense. Since machine would be the main use of electricity, using machine hours would make sense. Whereas the quality control person (indirect labor) is not using the machine, so using machine hours would not make sense for that cost. Depending on how the work is done, perhaps number of finished products inspected would be a more useful way to allocate those costs.