Your question is really too broad - read on and you'll see why, but I'd still like to help you. Look up Computer-to-Plate Platesetters on google for more information. Agfa is a major player in the field.
No. It's not the same as printing on paper. Printing plates are generally made of aluminium (sometimes even plastic), and have a water receptive surface and ink receptive surface to which the ink sticks. This is essential for the lithographic process to work.
There are several different technologies for these platesetters out there, but most use lasers for digital imaging of the plates. There are some which use plastic plates, and some which use metal plates which are then developed/chemically processed to fix the image and prepare the surface for printing. There are even chemical-free solutions these days.
There are too many different brands and technologies out there to mention specifics like resolution, or software used. It would really depend on the machine specs. I suggest you find a machine first, then look up the specs, even contact a dealer, or ask your printer what they use.