There are three main terms for testing by simultaneously 
acting multiple users (real or simulated): load, 
performance and stress testing. 

All performance and stress testings require workload 
definition as a part of the test. There may be no load, 
minimal load, normal load, above normal load or extreme 
load. So we will use the term "load testing" as a general 
category for all types of testing by simultaneously acting 
multiple users. The definition for load testing is: 

"Any type of testing where realistic (or hyper-realistic) 
workloads are characterized, simulated and submitted to the 
system under the test." 

Extreme loads are used in stress testing - to find the 
breaking point and bottlenecks of the tested system. 
Normal loads are used in performance testing - to ensure 
the acceptable level of performance characteristics like 
response time or request processing time under the 
estimated load. 
Minimal loads are often used in benchmark testing - to 
estimate user's experience. 

Anyway, load, not performance, is the shared characteristic 
across all these types of testing. 

In stress testing you should try to break the application 
by an extreme load and expose the bugs that are likely to 
appear under the stress, such as data corruption, buffer 
overflows, poor handling of resource depletion, deadlocks, 
race conditions etc. The fact that performance metrics such 
as response time can be measured during the stress testing 
is practically irrelevant to the purpose of stress testing. 
So stress testing and performance testing have totally 
different goals, which make it clear that stress testing is 
not a species of performance testing. 

Another reason for putting performance and stress under the 
load testing is another type of testing known as background 
testing. In background testing you use workloads (usually 
normal) to exercise the system under the test while you run 
functional and/or regression tests against the system. The 
goal of background testing is to test the functionality in 
more realistic conditions, i.e. with a realistic background 
workload, like the application will have in real use. 

But some sources treat Performance testing as a general 
category instead of Load testing. This approach is oriented 
towards test results (measured timings) while the using of 
Load testing as a category is concentrated on the test 
nature. We do not follow this approach, but it is rather 
widespread, so it should be mentioned. 

For example, Rational Unified Process defines these terms 
as follows : 
Performance testing is a class of tests implemented and 
executed to characterize and evaluate the performance 
related characteristics of the target-of-test such as the 
timing profiles, execution flow, response times, and 
operational reliability and limits. 

Included within this class are : 

Load testing - Verifies the acceptability of the target-of-
test's performance behaviour under the varying operational 
conditions (such as the number of users, number of 
transactions, etc) while the configuration remains 
constant. 

Stress testing - Verifies the acceptability of the target-
of-test's performance behaviour when abnormal or extreme 
conditions are encountered, such as diminished resources or 
extremely high number of users. 
Briefly: 
Performance testing is the overall process, 
Load testing checks if the system will support the expected 
conditions, 
Stress testing tries to break the system.