Denaturation- the process in which proteins lose their structure by the application of an external stress or compound. Coagulation- the process in which a fluid is changed in to a thickened mass (blood clotting).
Denaturation means, for example under the optimum temperature (specific temperature at which proteins work best) proteins function properly, but when the temperature increases over the optimum temperature they denature/destroy. They are destroyed. Coagulation means, reforming either into a thickened mass. Example, blood is a fluid, but when it clots it becomes thick in to masses. And yogurt the other example, milk is coagulated in to a thickened yogurt.