In the functional model, the real-word objects that the system relates to are represented by fields in data sources; either files or databases. The objects are implied.
In the object model, each object may have their own methods and data. Functions may exist locally within the objects or be ‘enacted’ by calls from objects to the methods of other objects. The details of the programs are unlikely to be precisely analogous but I hope the diagram shows the structural change.
‘Objects’ move from being “the elephant in the room” to being central to the design of the system. The system changes from an expression of a solution to a complex problem to being a model of the real-world problem domain, connected to solve a set of problems. The change is analogous to a move from a hard-wired office telephone network to a system of plug-boards that can be re-configured as the business changes form.
I created the diagram for my own use, so it is not thoroughly explained. I hope it is useful to someone but if I haven’t said enough to be understood then please ask for more.