Severance and unemployment, do they overlap?

My employer is paying severance in instalments and I am not sure whether to file now. I am in San Diego, in case local advice matters. I also wonder about the job-search requirement. Who should I ask before signing?

Before signing, I asked a friend who is a lawyer to look at the agreement. It was a short conversation and worth it.

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