How PhD classes are different from undergraduate?
Graduate-level classes are not necessarily any different than undergraduate classes, just more intense and more specialized.  Some graduate-level classes are just exactly the way that you describe.  Others have more of a "seminar" format, in which there is more reading and discussion, and in which students are expected to do part of the teaching---but at many institutions, there are also undergraduate classes like this.

The real heart of a Ph.D. program, however, is not the classes, but the research that students are involved with and should ultimately learn to initiate themselves.  Typically, Ph.D. programs start with a couple of years of intense classes, but then, once students have "qualified" (often by passing an oral or written examination), then classes become largely optional and you are expected to focus on research instead.