I don't believe there's a place for lies in a good relationship. You shouldn't hide things from your partner and the fact that you have to question whether or not it's right or wrong should be enough to tell you that it is. I have to talk to my ex on a regular basis because we have two children together and he has weekend visits with them. But the other people I dated, I would never consider talking with them and when they have tried to contact me, I told my husband about it.

One term I've heard for this phenomenon is "emotional infidelity." If it's not something I'd feel comfortable telling my partner about, I don't do it / talk about it with the other person. But we're married and in an explicitly committed, monogamous relationship. I'm not saying I never notice anyone else at all or that it doesn't feel good to have someone pay attention to me, but that kind of stuff is fleeting and meaningless--the commitment I made comes first, and nothing compares to what I feel for my husband. The love in my marriage comes first. I made the commitment with all my heart knowing that my husband is the best man I had ever met, that I love him with all my heart, and that he loves me with all his heart (I know, that's a lot of wholeheartedness, but it's true! ) The rules could be different for a different relationship, so figuring out what those ground rules are would be key. One helpful trick, by the way, is to remember why you broke up with the person in the first place, then to remember why you're with your current partner, and then, finally, to really imagine how your current partner would feel if he/she knew you were having conversations on the side.

I think it's cheating, you're doing something wrong if you feel you have to hide it from your SO

I would consider all secretary a bad thing, whether it leads to cheating or not.

The rule of thumb is usually if it feels like cheating to you, or if you need to ask, then it's probably considered cheating in your relationship. Everybody's relationships are different, so it'll be hard for anybody to really give you any objective advice.