...I asked the question because every law doesn't have an associated penalty that turns an illegal act into a criminal act.....
If an act or a thing is "illegal", performing that act or having the thing has legal consequences. In the context of entering property while armed, when that property is posted "no guns" the usual consequence with which people are concerned is a criminal charge -- often a form of criminal trespass. And in any case, the term "illegal" in context involve adverse consequences involving governmental action.
So we talk in terms of an illegal act, like criminal trespass, giving rise to prosecution by a governmental entity and criminal sanctions -- like incarceration or a fine. Certain other types of illegal conduct, such as building an addition to your house without proper permits, can give rise to different forms of sanctions imposed by governmental authority -- such as monetary civil penalties or even enforceable orders that the construction be demolished.
But in the world of civil wrongs, things like breach of contract or commission of a tort (like negligence), we don't refer to the conduct as "illegal." We refer to such conduct as creating a cause of action in the injured party, i. e., such conduct being actionable. The remedies must be pursued through actions in court initiated by a private party -- not the government.
Trespass can be both a crime and a tort. If criminal trespass is committed, the injured party calls the cops and the trespasser gets arrested. If one wants to pursue civil recourse for a trespass, he can file a lawsuit to demand payment for damage actually caused by the trespasser, or, in the case of a continuing trespass (e. g., a structure encroaching on your land), perhaps an injunction.
So in the case of a lawsuit seeking to redress a tortious trespass, if you win you'll get a judgement at some future time to the effect that the defendant owes you money or is ordered by the court to do something or to not do something. You then have to enforce the judgment.
Obviously, if someone comes into your store lawfully carrying a gun, and you've posted that you don't want someone with a gun in your store, a civil action for trespass is not a very useful remedy. The only recourse which is useful to you is, in some States, use the correct type of sign so you can call the cops and have the guy arrested, or, in other States, ask him to leave so that if he doesn't you can call the cops and have him arrested.
....I'm specifically talking about laws like Oklahoma, that says that a property owner can prohibit you from carrying and lists the steps that can be taken against you because you violated that prohibition. .... If you do not follow the law as written, are you doing something "against the law" or not? If it is not a violation of a law, how can a it be specifically used as the rationale for removal under penalty of a $250 citation?....
Because if you don't leave upon being asked, i. e., any permission you might have had to be on the private property has been withdrawn, you commit the crime under Oklahoma law of criminal trespass.