In performance testing we will try to keep more stress(i.e
maximum stress specified by client)on system and check
whether  the system performing the same way as for less
stress condition.whereas in Load testing we will keep stress
beyond the limit specified by client to check from which
point system's performance getting decrease.

Performance testing is the superset of load testing. Load 
testing involves testing how well the system is able to 
handle concurrent users or the load. Whereas performance 
testing comprises load as well as stress testing.

performance test consists of both load testing and stress 
testing  too . In load testing we check point at which 
system / application crashes . Let us take one example if 
we design website which can handle ( capacity ) 100 
concurrent user(100 users can performe the task on 
website ) . If we put 1000 concurrent user then system 
response gets down , it may crashes ,it's a saturation 
point .

Load testing mainly deals with the scalability/number of
users using the application
Performance Testing is done to understand the basestate of
the application. It includes response time Requests per
second etc