In a day and age when the use of technology is such an ingrained and instant form of daily communication, it can be confusing to figure out what types of conversation are appropriate or not, especially when you are in a committed relationship. Advice columnist Dear Wendy  offers up her two cents on the matter.
"Recently I found on my wife's phone inappropriate text messages to her ex-manager/friend that consisted of sexually explicit content. While it was not directed toward him in a sexual manner, it did consist of sexual banter.
While she says it was them 'joking,' I feel it was sexting — simply for the fact that the texts were graphic in content and words. She said that she was "teasing" him about his lusting after a certain female that they both worked with. But to me, a married woman/man should not engage in such 'banter' over mobile devices or computers or IMs or texts, especially when it is not with your spouse.
"This has caused trouble in our marriage because she doesn't see the wrong in it — even when I am telling her it hurts my feelings knowing she engages in such texts with someone other than I (and from what I recall, we have only sent sexts to one another a handful of times).
"As much as I try to explain to her that it is inappropriate for a married woman to engage in such behavior, I cannot get it through her head that it is 'sexting.'
"What say you in this matter?"
— Sexter's Husband
Well, first of all, why were you looking at her phone? Do you have reason to not trust her or is a desire to police her behavior a long-standing trend in your relationship? If it's the former, you need to address the trust issue. If it's the latter, you need to address where this need comes from.
Related: Dear Wendy: "Can I Ask My Party Guests to Pay For Their Own Dinners?" 
You've expressed to your wife that you feel that her text conversation, which was sexual in content, was inappropriate. You've told her that you feel it's "sexting." What was the response you wanted from her? An apology? A promise not to engage in such behavior again? Or was it most important that she agree with you that her text conversation was, indeed, "sexting," even if the content wasn't addressed to the recipient in a sexual manner? And if it was important for her to agree that her behavior qualified as sexting, would you consider that an admission of cheating? Is that, in the end, what you are seeking from her?
There must have been a reason you were looking at your wife's phone, and there must be a reason it's so important to you that there be some admission of sexting/cheating (if you consider sexting cheating). So what is that reason? In short: this incident seems a symptom of something bigger. What is that something? That is what the conversation with your wife should be about.
Related: Dear Wendy: "He Got Me Pregnant and Then Dumped Me" 
I can't speak to whether what your wife wrote was sexting or not without knowing what it was she said. Does it sounds inappropriate? Yes, probably? Maybe? But even that is up for debate. (Readers, what do you think? Is sending a message that is "sexually graphic in content and words" always sexting, regardless of its intent or how or to whom the message is delivered?) Regardless of what the general consensus is, if you felt offended and your wife isn't acknowledging your hurt feelings or taking any responsibility for them, you have to decide whether this is a battle worth fighting. If it is, why? If you can articulate what it is you feel is lacking — respect, trust, mutual understanding — you'll be in a better place to argue your point. And if you still can't find common ground, you may want to consider finding a couples' counselor to help you find and address the root of your problem (because, as I said, it's bigger than a text message with some sexual words).
Related: Dear Wendy: "I Hate My Sister's Fiancé"