How do you know if you're in Buda or Pest?

How can one distinguish between Buda and Pest, the two parts of Budapest? Are there any defining characteristics or landmarks that set them apart? For someone who is visiting the city for the first time, what are some telltale signs that would indicate they're in one part or the other? Is there a historical context that informs this distinction, and if so, how does it shape the modern-day identity of these two areas?