"the same" and "that particular one"
If you were to say, in casual conversation,
Tom and I drive the same car.
most Americans would assume you meant the same make and model. You wouldn't have to specify that you did not mean a single shared vehicle. In fact, if you did mean a single vehicle you would probably have to add information to the above example, or phrase the sentence differently, as in
Tom and I share a car.
"I'm driving a car just like his!"
You could reduce ambiguity by saying
I'm driving the same model of car.
or
I drive the same model.