I had a relationship of dating a co-worker from work and because I didn't disclose it , I was let go. I thought it was none of their business what happens outside of work. I guess not. I am wondering if they can say that I was terminated or what can be said?

Yes they can say exactly why you were let go if they want to.
They can say anything at all about your past work as long as it is true. Most don't any longer but there is no reason they can't

Would the company say something even if it makes them look bad as an employer?

I don't see why saying they let you go for dating a co worker makes them "look" bad. Many companies have rules against it. Others don't allow it within departments and so on.

They merely report you were fired, and if asked way, they state dating a co worker. That makes it sounds at least to the other company that there was a rule against it, and you and the other person violated it.

Did the other person also get fired, and if no, why not ?

I am not sure. He was a co worker and I was his supervisor. I didn't know that there was a company policy that I had to disclose it to management. They made it sound like I had it was a sexual relationship when we dated for a month and they just made this whole thing more than what it was. I just think I should have quit , but I had no idea that they would fire me based on my hard work and dedication.

I believe the reasoning behind the no dating policy is to protect the company from a sexual harassment lawsuit.

Since you two weren't equals, i.e. you were his supervisor, that could put you and the company in a bad spot if the relationship goes sour.

I just found out that he still has his job. How is that possible , when he is guilty of the same thing.

No, if you were the supervisor, the supervisor is considered more at fault

There are several reasons for not to date supervisor, favortism, harassment,there are things supervisor knows access to confidential information and now the person dating supervisor has easy access to as well... goes on and on.. HOPE THIS HELPS