Severance and unemployment, do they overlap? after 10 years as a janitorial supervisor

I was offered severance of 10 weeks after being let go as a janitorial supervisor and I am unsure how it affects benefits. There are 10 people counting on me, so I am trying to be careful. The agreement mentions a release and a payment schedule. Did you file straight away?

Some states only count certain kinds of severance. A local workforce centre could tell me which.