Severance and unemployment, do they overlap?

I was offered severance of 6 weeks after being let go as an event coordinator and I am unsure how it affects benefits. I am in Salt Lake City, in case local advice matters. I also wonder about the job-search requirement. Did you file straight away?

Thanks for writing this out. I went through something close to it 11 months ago, and it got easier once I kept a simple log of every call and form.