Difference between stress test and breakpoint test

From the workload point of view the approach is exactly the same, my understanding is:

• Stress test is about finding the first bottleneck, it's normally applied before deployment or even at early stages of development (see shift-left concept)
• Breakpoint (sometimes also called Capacity) test is about checking how much load the overall integrated environment can handle without issues and what is the slowest component which is a subject for scaling up/optimization.

More information:

• Software Performance Testing Types
• Performance Testing vs. Load Testing vs. Stress Testing
• What Is Performance Testing: Reviewing Load, Stress, & Capacity Testing