The VAERS system that Stockton refers to is a web site where anyone can report an adverse event following a vaccination. There is no initial verification that what is reported actually happened or that it was caused by a vaccine, but there can be an attempt for further investigation to determine if there is a true cause from a vaccine. From what has been looked into, there is nowhere near 20K deaths caused by the COVID vaccines acknowledged by the CDC, but that seems to be a popular talking point for the anti-vaccine side.
https://vaers.hhs.gov/
From the FAQ page:
Limitations of VAERS:
It is generally not possible to find out from VAERS data if a vaccine caused the adverse event
Reports submitted to VAERS often lack details and sometimes contains errors
Serious adverse events are more likely to be reported than non-serious events
Numbers of reports may increase in response to media attention and increased public awareness
VAERS data cannot be used to determine rates of adverse events