Jogging can lead to more injuries than walking if you are unprepared. Walking is low impact and low stress on the body so it is a go to exercise for many people with health problems.
Jogging can lead to foot, shin and knee problems (to name a few) if overused or done incorrectly.
However, jogging can lead to faster weight loss gains because it is more strenuous.
Before taking up jogging if you are new at it, see a running specialist and get a good pair of shoes recommended and join a running a group.
Running in a supervised group is a great way to get started if you’re not sure about it.