What can cause a 2 year old to walk fast instead of run? He doesn't seem to bend his knees when walking, so his legs seem to be stiffer when walking.

Hard to say. Children this young sometimes still have balance issues that affect how they walk. I suggest you consult with the pediatrician, who may recommend an evaluation by an occupational therapist or physical therapist. It could simply be a developmental phase, but it may reflect problems either with the legs themselves or with balance.