It depends. First of all from a legal standpoint, I believe there are only two states of being, single or married. If single, it could be you have always been single, or a divorce or death of a spouse could have made you single, but you are still single. I do not believe "divorced" is a legal marital state. Tax returns ask, single or married, for example. I am single. The way I became single is through a divorce. Now, when I introduce myself, I wouldn't say, "hi, my name is Tena and I am divorced", nor would I say, "hi, my name is Tena and I am single."
It would just be "hi, I my name is Tena, what's yours." If someone asked me if I was married, I would probably just say "no" or "no, I am not married." Now, in a dating situation I would certainly tell the person I was divorced rather than "just" single either on the first date or more likely, in the first stages of our even speaking to each other while developing some kind of a friendship. I am not trying to deceive anyone, by saying I am single rather than divorced, but the fact is I consider myself to be single, and it just happens that I am also divorced.
I believe a widow is also single, that person just happens to also be widowed just as I happen to be divorced.
So, in my opinion there can be many explanations for how we came to be single, but we are still single. So, though, it may be important for someone I am dating to know I have been married before, it is not necessary for everyone to know. This is why I sometimes list myself as single rather than divorced on this forum. I consider the fact that I am divorced to be an indication that I failed in marriage. I am not proud or happy about it and don't necessarily wish to share that with everyone.