Load and stress testing are subsets of performance testing.
Performance testing means how best something performs under a given benchmark. For example How mucn time you take to run 100 meters without carrying any load (no load is the benchmark) ?
Load testing is also performance testing but under various loads. The previous example if extended would be How much time you took to run the same 100mts but carrying a load of 50 kilos, 100 kilos .... ?
Stress testing is performance under stress conditions. Extending the same example as before How much time you took to run 100 meters with load or no load when a strong wind was blowing in opposite direction ?.
Extending performance, load.. testing to s/w or h/w application.
example
PERformance : 1000 txns per minute with 1000 users concurrent
Load : How many txns when 2000, 3000, 4000 concurrent users.
Stress : How many txns when 1000, 2000, 3000 concurrent users... under conditions like server memory very low, data transmission line poor, etc...