Severance is often given as a replacement of advance notice of a layoff (per the WARN Act). A company can either pay you 60 days of pay or give you a 60 day notice of a layoff. Most companies that I worked for, gave both an advanced warning and a severance package.
Severance pay has no effect on your unemployment. To the unemployment office it is just considered as part of your last paycheck. Always apply for unemployment the next business day after your last day at work.
Even if you are fired you can get unemployment. My last job fired me with no reason given. When the unemployment department called them to get a reason, they gave 3 different reasons from 3 different people. The unemployment department told me that by the answers they got from my former employer, they knew they were lying. The unemployment office had also dealt with my former employer in the past and I found out that they often made up reasons so that people would not get unemployment. I found out later that my former employer wanted to hire someone to replace me at $4.00 less an hour. They never found anyone.