sure. My town has a paid beach with lifeguard and a free beach without. It is illegal to swim on the free beach. It is not a crime. Worst case that happens is they kick you off the beach.
Lawyer here! Crime is the general term, and describes any offense against the people or the sovereign. Offenses are divided into severities, ranging from felony (worst) to infraction (least), with penalties to suit.
In this case, swimming on the free beach is probably an infraction, much like failing to use your turn signal. The worst penalty you’ll face in the usual case is a fine. But if you swim on the free beach, get yourself in trouble, and a rescue party has to come save you, the fact that it’s a “crime” now gives the state the ability to recover their costs from you afterwards.
Illegal means against the law or against the rules. A crime is a function of how severe your illegal action is.
Put it another way, people think if something is illegal, punishment for that must be a felony or something. But often times, it’s just an infraction so punishment is at most a fine or a minor action like getting kicked off the free beach
many people do think that since they make a big deal out of Airbnb and Uber doing something illegal - not realizing that the illegality of what they did is equivalent to getting a parking ticket.
In this case, swimming on the free beach is probably an infraction, much like failing to use your turn signal. The worst penalty you’ll face in the usual case is a fine. But if you swim on the free beach, get yourself in trouble, and a rescue party has to come save you, the fact that it’s a “crime” now gives the state the ability to recover their costs from you afterwards.