Exogenous shocks will result in asset price responses to outside information like an economic data surprise or Fed announcement. New information may lead to a revision in asset price valuations. Usually, there is evidence that asset markets will over-react to negative news and under-react to positive news. A bad news overreaction is caused by the need for markets to offer lower prices to attract new buyers. There is an under-reaction to good news because existing buyers will hold positions and a higher risk premium is not needed.
Endogenous shocks will cause asset prices to react to some event that is associated with actual price activity. It could be a change in prices from selling or buying pressure independent of an information announcement. An example would be a "flash crash" where order flow changes caused significant selling pressure. Obviously, these events are hard to predict and may be tied with an exogenous event. The endogenous event may be a feedback loop that starts with an information event.