Severance and unemployment, do they overlap?

I was offered severance of 16 weeks after being let go as a project coordinator and I am unsure how it affects benefits. This is my first time dealing with any of this. 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 last year, and it got easier once I kept a simple log of every call and form.