Severance and unemployment, do they overlap? after 10 years as a pharmacy technician

My employer is paying severance in instalments and I am not sure whether to file now. I worked as a pharmacy technician before this. The agreement mentions a release and a payment schedule. Who should I ask before signing?

Thanks for writing this out. I went through something close to it 14 months ago, and it settled down once I kept a simple log of every call and form.