In the United States all military law falls under something called the Uniform Code of Military Justice or UCMJ. In this case uniform doesn't mean clothing, uniform means that all branches of military service adhere to the same laws. And yes, it actually used to be different. The Navy and Marines under one set of laws, and the Army under another.
In many ways the UCMJ is stricter than civilian law, for example, adultery is a court martial offense under the UCMJ. Of course, this doesn't mean it doesn't happen, just as speeding still occurs even though it's against the law. Like speeding, don't get caught.
In other ways the UCMJ is much better, there is very little “gray area" or ambiguity, although the UCMJ allows for “Nonjudicial Punishment”. This gives commanders the leeway to impose less harsh penalties for minor offenses, where the same case in courts martial may be required to impose harsher penalties.