Performance testing - It is performed to evaluate the performance of components of a particular system in a specific situation. It very wide term. It includes: Load Testing, Stress Testing, capacity testing, volume testing, endurance testing, spike testing, scalability testing and reliability testing etc.
Load Testing is subset of performance testing. It is done by constantly increasing the load on the application under test till the time it reaches the threshold limit. The main goal of load testing is to identify the upper limit of the system in terms of database, hardware and network
Stress testing - It is done to evaluate the application's behaviour beyond normal or peak load conditions. It is basically testing the functionality of the application under high loads. Normally these are related to synchronization issues, memory leaks or race conditions etc