It is certainly possible for the same action to break multiple laws, and be chargeable as multiple crimes. For example, shooting and killing someone may be assault, assault with a deadly weapon, and murder all at the same time. For a different example a person who simply omits to file an income tax return may be guilty of both failure to file a required return, and failure to pay tax due, and in some cases failure to par required estimated tax due as well. For yet another example, driving well above the speed limit may be a violation of the speed limit law, and also careless driving, and possibly also reckless driving.
In the first case the assault etc may be lesser included offenses in the charge of murder. That means that they are automatically available to a jury (or judge) trying the accused, who can convict on one of the lesser included charges if they do not convict on the primary count. For the more general case, I don't know of any special term for the situation.
It is not usual to have law A which says "do not do X", and also law B which says "you must follow law A". There is no general principle against having such redundant laws, nor is there, in the US, any Constitutional rule against such laws. But legislatures do not normally bother to enact such redundant laws. Laws which will sometimes overlap in their coverage, but in some cases do not overlap are common.