Structures are collections of variables of different data types, while classes can also contain functions. The main differences are: structures have public access by default, are used for small data groups, and objects are stored on the stack. Classes have private access by default, are used for larger amounts of data with abstraction and inheritance, and objects are stored on the heap. Both allow variables, functions, constructors/destructors, and inheritance, but classes provide more robust features for object-oriented programming.