Is there any difference between a sm-P580 and a sm-T580 display?

Yes, a LCD display is compatible with both types. But when it comes to display type, you have more things to consider.

(Take LCD and LED screens as an example)

As you try to make the best choice for your professional and personal monitor needs, consider what features are necessary and most important to improving your work space and/or your gaming space. In many cases, an LED monitor holds the advantage due to its longer lifespan, better picture quality, thinner design, fast response time and more environmentally friendly construction. These qualities offset the higher initial price point that might have you considering an LCD option.