Severance and unemployment, do they overlap? - any advice?

I was offered severance of 5 weeks after being let go as a machine operator and I am unsure how it affects benefits. I would rather hear the honest version than the polite one. I also wonder about the job-search requirement. Who should I ask before signing?

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.