What happens on Jane's elbow?
when a skin is scratched, the internal medium of the body enter directly in contact with the external environment, this could lead bacteria (saprophytic bacteria which lives on the skin, or bacteria from another source) it will provoke an inflammatory reaction to these pathogens and so, a pus will be formed (generally composed by dead neutrophils and purulent bacteria).
What happened on Sarah's knee?
The knee was just bruised, there's not skin scratching, it is still intact, so bacteria cannot go into the body through this injury. It just takes colors (red, blue, then yellow due to the rupture of capillaries which release blood, then will be degraded in bilirubin)