There's a good article on the differences here.
Here's a search on dye sublimation printers so you can see which models they are.
Sony's DPP-EX50 Picture Station is a dye sublimation printer. Steve's Digicams looks at the cost per page. He says:
The DPP-EX50 sells for about $180 and the ribbon and paper averages about $0.60 per print when making 4 x 6" postcard size prints.That price per print seems high to me when I can get commercial digital prints at Walgreen's for $0.29. Better yet, I can use Picasa and upload them to Wal-Mart and have them waiting for me for $0.19 ($0.17 if you use Sam's Club). And remember, the pickup location can be at ANY Wal-Mart so you can send them to your mother's home town.