Generally speaking, the legal community in Arizona refers to a "wet reckless" as a "confirming reckless driving plea offer." A "conforming reckless driving plea offer" ("conforming reckless," herein) carries many of the same penalties as a DUI, however there is usually no interlock requirement. TI agree with what the other lawyers have posted on this issue. However, it's important to understand that because a "conforming reckless" carries many of the same penalties, many lawyers, including myself, try to negotiate a full-blown dismissal or traditional reckless driving resolution. Each case is different. The probability of obtaining a dismissal, reckless driving, or conforming reckless driving ("wet reckless"), depend on many factors. The most important factor is whether the State's case has weaknesses in it that make the prosecutor concerned that the prosecutor may lose the case in front of a jury. Having said that, other factors are usually also very important: the policies of the prosecutorial agency involved, the defendant's background, the judge, etc. Some prosecutors will never care about the defendant's background, while others will. Having an experienced DUI lawyer is important because that lawyer can more effectively find weaknesses in the prosecutor's case (if they exist) and can more persuasively present your background and the legal issues to the prosecutor, jury, or judge. Thus, whether your goal is negotiation or litigation, having an experienced DUI lawyer is necessary.
There's no such thing as a "wet and reckless" in Arizona. There is however a crime of reckless driving. In terms of the difference between Reckless driving and DUI they both carry 8 points on MVD driving record, but DUI is a higher class of offense and carries certain mandatory minimum penalties that a reckless driving conviction does not carry. For example, even a regular first offense DUI carries a mandatory minimum 1 day jail with an additional 9 days suspended upon completion of alcohol treatment.
When there is a potential defense to the DUI such as borderline blood alcohol level. Sometimes a prosecutor may offer a reckless driving plea but with similar penalties as DUI such as including the alcohol counseling. I have heard this colloquially called a "wet reckless" to refer to the fact that alcohol counseling is being ordered on a reckless driving.