If I have been divorced for 14 years now, should I file Single vs. divorced? is there really a difference?

No difference.  Divorced is not a filing status.  You are Single.  

Divorced is not a filing status on a tax return.   The software asks if you are married or divorced, etc. but that is only to navigate you to certain questions regarding alimony, etc.   If you are not supporting/custodial parent of  dependent children then your filing status is Single.