The difference between risk mitigation and risk contingency is very thin...
Risk mitigation (sometimes referred to as risk response) is what will you do should the risk materializes. Let's assume, for example, that there was a union strike, and you have no more people working. This will delay the project. Whatever action you do to handle the situation at this point would be called risk mitigation. It's like dealing with the aftermath. A risk mitigation plan is improvised and is done when the risk materializes.
Risk contingency, on the other hand, is about planning what to do should a risk materialize. For example, you are expecting that there will be a strike, and that all your workers will stop working. Your risk contingency plan will include that should a strike happen, you will hire a team from elsewhere.