While some objects I create are modelling real world objects, would not pre-OOP code do the same?
I would say not. OOP ties down the relationship between things (properties/objects) and what they can do/can be done to them (methods), whereas functionalprocedural programming doesn't do this (aside from, to a small degree, when using strict typing). A model isn't just about defining discrete parts and processes, it's also about defining how they fit together, and OOP is particularly good at this.