this is my take on it:
Divorced means you were once married and now aren’t in the eyes of the law - this is not the same as an anullment which means a marrage never took place (for one reason or another).
single means never married (including anullments)
Some people don’t take divorces as valid ends of a marrage. Just having single, married, and widowed would leave a divorced person to state single but some people believe that you are still married (even though you don’t see each other) which would make your statement a falsehood as far as they are concerned. the ‘divorces’ catagory lets the readed decide which catagory you are in.
There is a diffrence to people, just ask someone who is dating how they would react if they found out the person they 1st assumed was single was really divorced - not everyone would care but many will