APM typically refers to the practice of instrumenting APIs within a backend application, and getting visibility of the golden signals (and more) associated with these APIs.
Error budget helps in prioritization and in ensuring most critical problems are dealt with first. It also prevents the accumulation of the technical debt that can slow down the development over time.
Engineering teams create error budget policies to protect customers from repeated misses in SLOs.
Here’s an example of an error budget policy by Google SRE.