Depending upon where you live, real estate law determines what (if any) portion of a beach (or a freshwater lake) can be privately owned.
As for the seashore, in some states private ownership is down to the "mean high tide" line, in others it is "mean low tide" line. There are also places where the ENTIRE beach is owned by the state or federal government, or a Native American Tribe. Certainly in mooring and wharf areas, there are private owners of the appurtenant structures and perhaps the land beneath them.
Where the laws provide for beach ownership, taking things from the beach (such as naturally occurring shellfish, driftwood, flotsam or jetsam) is considered theft of personal property, but only if taken within the prescribed tidal area that is privately owned. Similarly, walking on such areas is considered "trespass", although not usually criminal unless fenced or properly posted with warning signs.