Jogging shoes and running shoes are designed for different activities, so you can bet that there are some major differences between the two.
Jogging shoes are made for a slower pace and less strenuous activity than running shoes, so they usually feature less cushioning and support. These are great for those who are new to exercise or those who are not training for a specific event (like a 5k or half marathon).
Running shoes are designed for a faster pace and more intense activity. They have lots of cushioning (to absorb the shock that comes with the impact of running) and are generally more responsive, which can help runners improve their performance.