AWS's definition of a stress test as stated in the document you provided is "when a test sends a large volume of legitimate or test traffic to a specific intended target application" while DDOS tests are defined in the same document as "Tests that purposefully attempt to overwhelm the target and/or infrastructure with packet or connection flooding attacks, reflection and complexity attacks, or other large volumes of traffic are not considered network stress tests but are considered distributed denial of service (DDoS) tests."
The main difference between them is that one is purposely attempting to overload the target/infrastructure with attacks. Not legitimate traffic but traffic that is intended to maliciously deny the service of legitimate traffic. Stress/load testing is testing your infrastructure with legitimate traffic that you are expecting and monitoring your environment for how it handles that traffic. There can be some confusion since both can cause denial-of-service but one is done maliciously via attacking methods (syn flooding / amplification / reflection / ICMP flood etc) and the other is testing your target/infrastructure with legitimate and expected traffic to see how your environment can handle it.
I hope this provides some clarity!
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