Severance and unemployment, do they overlap? - what worked for you?

I was offered severance of 10 weeks after being let go as a security officer and I am unsure how it affects benefits. I am in Seattle, in case local advice matters. The agreement mentions a release and a payment schedule. How did your state treat it?

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.